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Name: ________________________ Class: ___________________ Date: __________ ID: A
1
Nuclear Honors Practice
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
____ 1. Balance the following equation: 88226 Ra
86222 Rn____
a. 24 He c. 1
1H
b. 01n d. 1
0 e
____ 2. Balance the following equation: 92238 U+ ____ 92
239 U
a. 24 He c. 1
1H
b. 01n d. 1
0 e
____ 3. Balance the following equation: 49Be+ 2
4 He 612 C + ____
a. 24 He c. 1
1H
b. 01n d. 1
0 e
____ 4. Balance the following equation: 37Li+ ____ 2
4 He + 24 He
a. 24 He c. 1
1H
b. 01n d. 1
0 e
____ 5. Balance the following equation: 93239 Np ____ + 1
0 e
a. 90239 Th c. 94
239 Pu
b. 92239 U d. 94
238 Pu
____ 6. How many half-lives are required for three-fourths of the nuclei of one isotope in a sample to decay?
a.34
c. 2
b.32
d. 3
____ 7. What is the half-life of an isotope if 125 g of a 500 g sample of the isotope remain after 3.0 years?a. 1.5 years c. 3.5 yearsb. 2.5 years d. 4.5 years
Name: ________________________ ID: A
2
____ 8. According to the table below, if a rock contains 25% as much uranium-235 as rocks being formed today, how old is the rock?
Nuclide Half-Life (years)
carbon-14 5.71 103
potassium-40 1.26 109
radium-226 1.60 103
thorium-230 7.54 104
uranium-235 7.04 108
a. 7.04 108 years c. 2.84 109 yearsb. 3.55 108 years d. 1.41 109 years
____ 9. What particle is needed to complete this nuclear reaction?
98251 Cf 96
247 Cm + _____
a. 24 He c. 1
1 H
b. 10 e d. 0
1 n
____ 10. When radium-226 (atomic number 88) decays by emitting an alpha particle, it becomes ____.a. polonium-222 c. radium-222b. polonium-224 d. radon-222
____ 11. What particle does nickel-57 emit when it decays to cobalt-57? (Remember to evaluate atomic numbers)a. neutron c. protonb. positron d. alpha particle
____ 12. What particle is needed to complete the following equation?
714 N + ____ 6
14 C + 11 H
a. 01 n c. 2
4 He
b. 10 e d. 1
0 e
____ 13. To what element does polonium-208 (atomic number 84) decay when it emits an alpha particle?
a. 82210 Pb c. 82
204 Pb
b. 82210 Po d. 86
214 Rn
Short Answer
14. Complete the following nuclear reaction:
92
_U 2
4He + _231 __
15. If the half-life of a radioactive material is 6 years, how many years will it take for one half of the original amount of material to decay?
16. After 56 days, 4 g of phosphorus-32 has decayed to 0.25 g. What is the half-life of phosphorus-32?
17. The radioisotope radon-222 has a half-life of 3.8 days. How much of a 73.9-g sample of radon-222 would be left after approximately 23 days?
Name: ________________________ ID: A
3
18. If the half-life of sodium-24 is 15 hours, how much remains from a 25.0-g sample after 60 hours?
19. What is the half-life of phosphorus-32 if, after 42 days, 0.375 g remains from a 3.00-g starting sample?
20. The concentration of carbon-14 in a piece of wood from an ancient burial mound indicates that ten half-lives of this radioisotope have passed. If the half-life (t 1 2 ) for carbon-14 is 5730 years, approximately how many
years ago did this sample of wood die?
Problem
21. Calculate the mass defect and the binding energy/nucleon of the nuclide 815 O, which has a mass of
15.00306565 amu. The mass of a proton is 1.007 276 47 amu and the mass of a neutron is 1.008 664 90. One amu = 1.6605 10–27 kg and the speed of light is 3.00 108 m/s.
22. Write the nuclear equation for each of the following reactions. Refer to a periodic table.
a. the alpha decay of 88226 Ra
b. the beta decay of 1739 Cl
c. the positron emission of 1530 P
23. Phosphorus-32 has a half-life of 14.3 days. How many milligrams of phosphorus-32 remain after 71.5 days if you start with 4.00 mg of the isotope?
24. What is the half-life of an isotope if after 2.00 weeks you have 31.25 g remaining from a 250.0 g starting sample size?
Essay
25. Manganese-52 has a half-life of 6 days. If the amount of manganese-52 in a sample is 32 g, how much manganese-52 will remain after 24 days?
26. After 252 days, a 12.0-g starting sample of the radioisotope scandium-46 contains only 1.5 g of the isotope. What is the half-life of scandium-46? Explain your reasoning.
ID: A
1
Nuclear Honors PracticeAnswer Section
MULTIPLE CHOICE
1. ANS: A PTS: 1 DIF: II REF: 1OBJ: 4
2. ANS: B PTS: 1 DIF: II REF: 1OBJ: 4
3. ANS: B PTS: 1 DIF: II REF: 1OBJ: 4
4. ANS: C PTS: 1 DIF: II REF: 1OBJ: 4
5. ANS: C PTS: 1 DIF: II REF: 1OBJ: 4
6. ANS: CSolution: x number of half-lives
14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
PTS: 1 DIF: I REF: 2 OBJ: 3 7. ANS: A
Solution:
fraction of original sample 500 g125 g
0.250 or14
x the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
14
, x 2
3.0 yrs 2 half-lifes, 1 half-life 1.5 yrs
PTS: 1 DIF: III REF: 2 OBJ: 3 8. ANS: D
Solution: x number of half-lives
25% 14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
2 half-lives 7.04 108 yrs
1 half-life 14.08 108 yrs 1.14 109 yrs
PTS: 1 DIF: III REF: 2 OBJ: 4
ID: A
2
9. ANS: A PTS: 1 DIF: L2 REF: p. 801OBJ: 25.2.1
10. ANS: D PTS: 1 DIF: L2 REF: p. 800 | p. 804OBJ: 25.1.2 | 25.2.1
11. ANS: B PTS: 1 DIF: L2 REF: p. 801OBJ: 25.2.1
12. ANS: A PTS: 1 DIF: L3 REF: p. 803 | p. 804OBJ: 25.2.1
13. ANS: C PTS: 1 DIF: L3 REF: p. 800 | p. 804OBJ: 25.1.2 | 25.2.1
SHORT ANSWER
14. ANS:
92235 U 2
4 He + 90231 Th
PTS: 1 DIF: L2 REF: p. 800 OBJ: 25.2.1 15. ANS:
6 years
PTS: 1 DIF: L1 REF: p. 804 OBJ: 25.2.2 16. ANS:
14 days
PTS: 1 DIF: L2 REF: p. 804 | p. 806 OBJ: 25.2.2
17. ANS: 23 days/3.8 days = approximately 6 half-lives have passed.73.9 g (0.5)^6 = 1.2 g remaining.
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
18. ANS: number of half-lives = 60 hours / 15 hours = 4
remaining = 25.0 12
4 1.563 g
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
19. ANS: 0.375g3.00g
18 1
2
3
3 = number of half-lives (exponent of 1/2)
42 days / 3 half-lives = 14 days (the half-life time)
PTS: 1 DIF: L3 REF: p. 804 OBJ: 25.2.2
ID: A
3
20. ANS: 57,300 years ago
PTS: 1 DIF: L3 REF: p. 806 OBJ: 25.2.2
PROBLEM
21. ANS: mass defect = 8(mass of proton) + 7(mass of neutron) mass of nuclide
= 8(1.007 276 47 amu) +7(1.008 664 90 amu) 15.00306565 amu= 8.05821176 amu + 7.0606543 amu 15.00306565 amu= 15.11886606 amu 15.00306565 amu
mass defect = 0.11580041 amubinding energy/nucleon = (0.11580041 amu)(1.6605 1027 kg/amu)(3 108) ( m/s)2/15 nucleons = 3.846e–021 J/nucleonbinding energy/nucleon = 3.846e–021 J/nucleon
PTS: 1 DIF: III REF: 1 OBJ: 1 22. ANS:
a. 88226 Ra
24 He
86222 Rn
b. 1739 Cl 1
e e 1839 Ar
c. 1530 P 1
0 e 1530 Si
PTS: 1 DIF: II REF: 1 OBJ: 4 23. ANS:
0.125 mgSolution:
7.15 days 1 half-life14.3 days
5 half-lives
4.00 mg 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
5
0.125 mg
PTS: 1 DIF: III REF: 2 OBJ: 3
ID: A
4
24. ANS: half-life = 4.67 daysSolution:
fraction of original 31.25 g250.0 g
0.125 or18
x = the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
18
, x 3
2.00 weeks 3 half-lives
2.00 weeks3 half-lives
0.667 weekshalf-life
7 daysweek
4.67 days
PTS: 1 DIF: III REF: 2 OBJ: 3
ESSAY
25. ANS: 24 days is the equivalent of 4 half-life periods. 1/16 of the original sample remains. 1/16 of 32 g is 2 g. There are 2 grams remaining.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
26. ANS: One-eighth of the sample remains, so the isotope must have decayed through 3 half-lives. Three half-lives = 252 days, so one half-life = 252/3 days. Therefore, the half-life of scandium-46 is 84 days.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
Name: ________________________ Class: ___________________ Date: __________ ID: B
1
Nuclear Honors Practice
Short Answer
1. If the half-life of sodium-24 is 15 hours, how much remains from a 25.0-g sample after 60 hours?
2. After 56 days, 4 g of phosphorus-32 has decayed to 0.25 g. What is the half-life of phosphorus-32?
3. The radioisotope radon-222 has a half-life of 3.8 days. How much of a 73.9-g sample of radon-222 would be left after approximately 23 days?
4. The concentration of carbon-14 in a piece of wood from an ancient burial mound indicates that ten half-lives of this radioisotope have passed. If the half-life (t 1 2 ) for carbon-14 is 5730 years, approximately how many
years ago did this sample of wood die?
5. What is the half-life of phosphorus-32 if, after 42 days, 0.375 g remains from a 3.00-g starting sample?
6. If the half-life of a radioactive material is 6 years, how many years will it take for one half of the original amount of material to decay?
7. Complete the following nuclear reaction:
92
_U 2
4He + _231 __
Problem
8. Phosphorus-32 has a half-life of 14.3 days. How many milligrams of phosphorus-32 remain after 71.5 days if you start with 4.00 mg of the isotope?
9. Write the nuclear equation for each of the following reactions. Refer to a periodic table.
a. the alpha decay of 88226 Ra
b. the beta decay of 1739 Cl
c. the positron emission of 1530 P
10. What is the half-life of an isotope if after 2.00 weeks you have 31.25 g remaining from a 250.0 g starting sample size?
11. Calculate the mass defect and the binding energy/nucleon of the nuclide 815 O, which has a mass of
15.00306565 amu. The mass of a proton is 1.007 276 47 amu and the mass of a neutron is 1.008 664 90. One amu = 1.6605 10–27 kg and the speed of light is 3.00 108 m/s.
Essay
12. After 252 days, a 12.0-g starting sample of the radioisotope scandium-46 contains only 1.5 g of the isotope. What is the half-life of scandium-46? Explain your reasoning.
13. Manganese-52 has a half-life of 6 days. If the amount of manganese-52 in a sample is 32 g, how much manganese-52 will remain after 24 days?
Name: ________________________ ID: B
2
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
____ 14. When radium-226 (atomic number 88) decays by emitting an alpha particle, it becomes ____.a. polonium-224 c. polonium-222b. radon-222 d. radium-222
____ 15. To what element does polonium-208 (atomic number 84) decay when it emits an alpha particle?
a. 86214 Rn c. 82
210 Po
b. 82204 Pb d. 82
210 Pb
____ 16. Balance the following equation: 92238 U+ ____ 92
239 U
a. 01n c. 2
4 He
b. 10 e d. 1
1H
____ 17. Balance the following equation: 37Li+ ____ 2
4 He + 24 He
a. 24 He c. 1
1H
b. 10 e d. 0
1n
____ 18. What particle does nickel-57 emit when it decays to cobalt-57? (Remember to evaluate atomic numbers)a. proton c. alpha particleb. positron d. neutron
____ 19. What particle is needed to complete the following equation?
714 N + ____ 6
14 C + 11 H
a. 10 e c. 1
0 e
b. 01 n d. 2
4 He
____ 20. What particle is needed to complete this nuclear reaction?
98251 Cf 96
247 Cm + _____
a. 01 n c. 2
4 He
b. 10 e d. 1
1 H
____ 21. How many half-lives are required for three-fourths of the nuclei of one isotope in a sample to decay?
a. 3 c.34
b. 2 d.32
Name: ________________________ ID: B
3
____ 22. According to the table below, if a rock contains 25% as much uranium-235 as rocks being formed today, how old is the rock?
Nuclide Half-Life (years)
carbon-14 5.71 103
potassium-40 1.26 109
radium-226 1.60 103
thorium-230 7.54 104
uranium-235 7.04 108
a. 1.41 109 years c. 2.84 109 yearsb. 7.04 108 years d. 3.55 108 years
____ 23. Balance the following equation: 93239 Np ____ + 1
0 e
a. 94239 Pu c. 92
239 U
b. 94238 Pu d. 90
239 Th
____ 24. What is the half-life of an isotope if 125 g of a 500 g sample of the isotope remain after 3.0 years?a. 2.5 years c. 4.5 yearsb. 1.5 years d. 3.5 years
____ 25. Balance the following equation: 49Be+ 2
4 He 612 C + ____
a. 01n c. 1
0 e
b. 24 He d. 1
1H
____ 26. Balance the following equation: 88226 Ra 86
222 Rn____
a. 11H c. 2
4 He
b. 01n d. 1
0 e
ID: B
1
Nuclear Honors PracticeAnswer Section
SHORT ANSWER
1. ANS: number of half-lives = 60 hours / 15 hours = 4
remaining = 25.0 12
4 1.563 g
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
2. ANS: 14 days
PTS: 1 DIF: L2 REF: p. 804 | p. 806 OBJ: 25.2.2
3. ANS: 23 days/3.8 days = approximately 6 half-lives have passed.73.9 g (0.5)^6 = 1.2 g remaining.
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
4. ANS: 57,300 years ago
PTS: 1 DIF: L3 REF: p. 806 OBJ: 25.2.2 5. ANS:
0.375g3.00g
18 1
2
3
3 = number of half-lives (exponent of 1/2)
42 days / 3 half-lives = 14 days (the half-life time)
PTS: 1 DIF: L3 REF: p. 804 OBJ: 25.2.2 6. ANS:
6 years
PTS: 1 DIF: L1 REF: p. 804 OBJ: 25.2.2 7. ANS:
92235 U 2
4 He + 90231 Th
PTS: 1 DIF: L2 REF: p. 800 OBJ: 25.2.1
ID: B
2
PROBLEM
8. ANS: 0.125 mgSolution:
7.15 days 1 half-life14.3 days
5 half-lives
4.00 mg 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
5
0.125 mg
PTS: 1 DIF: III REF: 2 OBJ: 3 9. ANS:
a. 88226 Ra 2
4 He 86222 Rn
b. 1739 Cl 1
e e 1839 Ar
c. 1530 P 1
0 e 1530 Si
PTS: 1 DIF: II REF: 1 OBJ: 4 10. ANS:
half-life = 4.67 daysSolution:
fraction of original 31.25 g250.0 g
0.125 or18
x = the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
18
, x 3
2.00 weeks 3 half-lives
2.00 weeks3 half-lives
0.667 weekshalf-life
7 daysweek
4.67 days
PTS: 1 DIF: III REF: 2 OBJ: 3
ID: B
3
11. ANS: mass defect = 8(mass of proton) + 7(mass of neutron) mass of nuclide
= 8(1.007 276 47 amu) +7(1.008 664 90 amu) 15.00306565 amu= 8.05821176 amu + 7.0606543 amu 15.00306565 amu= 15.11886606 amu 15.00306565 amu
mass defect = 0.11580041 amubinding energy/nucleon = (0.11580041 amu)(1.6605 1027 kg/amu)(3 108) ( m/s)2/15 nucleons = 3.846e–021 J/nucleonbinding energy/nucleon = 3.846e–021 J/nucleon
PTS: 1 DIF: III REF: 1 OBJ: 1
ESSAY
12. ANS: One-eighth of the sample remains, so the isotope must have decayed through 3 half-lives. Three half-lives = 252 days, so one half-life = 252/3 days. Therefore, the half-life of scandium-46 is 84 days.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
13. ANS: 24 days is the equivalent of 4 half-life periods. 1/16 of the original sample remains. 1/16 of 32 g is 2 g. There are 2 grams remaining.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
MULTIPLE CHOICE
14. ANS: B PTS: 1 DIF: L2 REF: p. 800 | p. 804OBJ: 25.1.2 | 25.2.1
15. ANS: B PTS: 1 DIF: L3 REF: p. 800 | p. 804OBJ: 25.1.2 | 25.2.1
16. ANS: A PTS: 1 DIF: II REF: 1OBJ: 4
17. ANS: C PTS: 1 DIF: II REF: 1OBJ: 4
18. ANS: B PTS: 1 DIF: L2 REF: p. 801OBJ: 25.2.1
19. ANS: B PTS: 1 DIF: L3 REF: p. 803 | p. 804OBJ: 25.2.1
20. ANS: C PTS: 1 DIF: L2 REF: p. 801OBJ: 25.2.1
ID: B
4
21. ANS: BSolution: x number of half-lives
14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
PTS: 1 DIF: I REF: 2 OBJ: 3 22. ANS: A
Solution: x number of half-lives
25% 14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
2 half-lives 7.04 108 yrs
1 half-life 14.08 108 yrs 1.14 109 yrs
PTS: 1 DIF: III REF: 2 OBJ: 4 23. ANS: A PTS: 1 DIF: II REF: 1
OBJ: 4 24. ANS: B
Solution:
fraction of original sample 500 g125 g
0.250 or14
x the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
14
, x 2
3.0 yrs 2 half-lifes, 1 half-life 1.5 yrs
PTS: 1 DIF: III REF: 2 OBJ: 3 25. ANS: A PTS: 1 DIF: II REF: 1
OBJ: 4 26. ANS: C PTS: 1 DIF: II REF: 1
OBJ: 4
Name: ________________________ Class: ___________________ Date: __________ ID: C
1
Nuclear Honors Practice
Problem
1. Calculate the mass defect and the binding energy/nucleon of the nuclide 815 O, which has a mass of
15.00306565 amu. The mass of a proton is 1.007 276 47 amu and the mass of a neutron is 1.008 664 90. One amu = 1.6605 10–27 kg and the speed of light is 3.00 108 m/s.
2. What is the half-life of an isotope if after 2.00 weeks you have 31.25 g remaining from a 250.0 g starting sample size?
3. Write the nuclear equation for each of the following reactions. Refer to a periodic table.
a. the alpha decay of 88226 Ra
b. the beta decay of 1739 Cl
c. the positron emission of 1530 P
4. Phosphorus-32 has a half-life of 14.3 days. How many milligrams of phosphorus-32 remain after 71.5 days if you start with 4.00 mg of the isotope?
Essay
5. Manganese-52 has a half-life of 6 days. If the amount of manganese-52 in a sample is 32 g, how much manganese-52 will remain after 24 days?
6. After 252 days, a 12.0-g starting sample of the radioisotope scandium-46 contains only 1.5 g of the isotope. What is the half-life of scandium-46? Explain your reasoning.
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
____ 7. When radium-226 (atomic number 88) decays by emitting an alpha particle, it becomes ____.a. polonium-224 c. radium-222b. radon-222 d. polonium-222
____ 8. Balance the following equation: 88226 Ra 86
222 Rn____
a. 10 e c. 0
1n
b. 24 He d. 1
1H
Name: ________________________ ID: C
2
____ 9. According to the table below, if a rock contains 25% as much uranium-235 as rocks being formed today, how old is the rock?
Nuclide Half-Life (years)
carbon-14 5.71 103
potassium-40 1.26 109
radium-226 1.60 103
thorium-230 7.54 104
uranium-235 7.04 108
a. 1.41 109 years c. 7.04 108 yearsb. 2.84 109 years d. 3.55 108 years
____ 10. To what element does polonium-208 (atomic number 84) decay when it emits an alpha particle?
a. 82210 Pb c. 82
204 Pb
b. 86214 Rn d. 82
210 Po
____ 11. Balance the following equation: 37Li+ ____ 2
4 He + 24 He
a. 24 He c. 1
1H
b. 01n d. 1
0 e
____ 12. Balance the following equation: 93239 Np ____ + 1
0 e
a. 94239 Pu c. 94
238 Pu
b. 92239 U d. 90
239 Th
____ 13. How many half-lives are required for three-fourths of the nuclei of one isotope in a sample to decay?a. 3 c. 2
b.34
d.32
____ 14. What particle is needed to complete this nuclear reaction?
98251 Cf 96
247 Cm + _____
a. 11 H c. 1
0 e
b. 24 He d. 0
1 n
____ 15. What particle is needed to complete the following equation?
714 N + ____ 6
14 C + 11 H
a. 10 e c. 0
1 n
b. 24 He d. 1
0 e
____ 16. What particle does nickel-57 emit when it decays to cobalt-57? (Remember to evaluate atomic numbers)a. alpha particle c. neutronb. proton d. positron
Name: ________________________ ID: C
3
____ 17. Balance the following equation: 92238 U+ ____ 92
239 U
a. 10 e c. 1
1H
b. 01n d. 2
4 He
____ 18. Balance the following equation: 49Be+ 2
4 He 612 C + ____
a. 24 He c. 1
0 e
b. 01n d. 1
1H
____ 19. What is the half-life of an isotope if 125 g of a 500 g sample of the isotope remain after 3.0 years?a. 4.5 years c. 1.5 yearsb. 2.5 years d. 3.5 years
Short Answer
20. Complete the following nuclear reaction:
92
_U 2
4He + _231 __
21. After 56 days, 4 g of phosphorus-32 has decayed to 0.25 g. What is the half-life of phosphorus-32?
22. If the half-life of a radioactive material is 6 years, how many years will it take for one half of the original amount of material to decay?
23. The radioisotope radon-222 has a half-life of 3.8 days. How much of a 73.9-g sample of radon-222 would be left after approximately 23 days?
24. If the half-life of sodium-24 is 15 hours, how much remains from a 25.0-g sample after 60 hours?
25. The concentration of carbon-14 in a piece of wood from an ancient burial mound indicates that ten half-lives of this radioisotope have passed. If the half-life (t 1 2 ) for carbon-14 is 5730 years, approximately how many
years ago did this sample of wood die?
26. What is the half-life of phosphorus-32 if, after 42 days, 0.375 g remains from a 3.00-g starting sample?
ID: C
1
Nuclear Honors PracticeAnswer Section
PROBLEM
1. ANS: mass defect = 8(mass of proton) + 7(mass of neutron) mass of nuclide
= 8(1.007 276 47 amu) +7(1.008 664 90 amu) 15.00306565 amu= 8.05821176 amu + 7.0606543 amu 15.00306565 amu= 15.11886606 amu 15.00306565 amu
mass defect = 0.11580041 amubinding energy/nucleon = (0.11580041 amu)(1.6605 1027 kg/amu)(3 108) ( m/s)2/15 nucleons = 3.846e–021 J/nucleonbinding energy/nucleon = 3.846e–021 J/nucleon
PTS: 1 DIF: III REF: 1 OBJ: 1 2. ANS:
half-life = 4.67 daysSolution:
fraction of original 31.25 g250.0 g
0.125 or18
x = the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
18
, x 3
2.00 weeks 3 half-lives
2.00 weeks3 half-lives
0.667 weekshalf-life
7 daysweek
4.67 days
PTS: 1 DIF: III REF: 2 OBJ: 3 3. ANS:
a. 88226 Ra 2
4 He 86222 Rn
b. 1739 Cl 1
e e 1839 Ar
c. 1530 P 1
0 e 1530 Si
PTS: 1 DIF: II REF: 1 OBJ: 4
ID: C
2
4. ANS: 0.125 mgSolution:
7.15 days 1 half-life14.3 days
5 half-lives
4.00 mg 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
5
0.125 mg
PTS: 1 DIF: III REF: 2 OBJ: 3
ESSAY
5. ANS: 24 days is the equivalent of 4 half-life periods. 1/16 of the original sample remains. 1/16 of 32 g is 2 g. There are 2 grams remaining.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
6. ANS: One-eighth of the sample remains, so the isotope must have decayed through 3 half-lives. Three half-lives = 252 days, so one half-life = 252/3 days. Therefore, the half-life of scandium-46 is 84 days.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
MULTIPLE CHOICE
7. ANS: B PTS: 1 DIF: L2 REF: p. 800 | p. 804OBJ: 25.1.2 | 25.2.1
8. ANS: B PTS: 1 DIF: II REF: 1OBJ: 4
9. ANS: ASolution: x number of half-lives
25% 14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
2 half-lives 7.04 108 yrs
1 half-life 14.08 108 yrs 1.14 109 yrs
PTS: 1 DIF: III REF: 2 OBJ: 4 10. ANS: C PTS: 1 DIF: L3 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1 11. ANS: C PTS: 1 DIF: II REF: 1
OBJ: 4
ID: C
3
12. ANS: A PTS: 1 DIF: II REF: 1OBJ: 4
13. ANS: CSolution: x number of half-lives
14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
PTS: 1 DIF: I REF: 2 OBJ: 3 14. ANS: B PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1 15. ANS: C PTS: 1 DIF: L3 REF: p. 803 | p. 804
OBJ: 25.2.1 16. ANS: D PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1 17. ANS: B PTS: 1 DIF: II REF: 1
OBJ: 4 18. ANS: B PTS: 1 DIF: II REF: 1
OBJ: 4 19. ANS: C
Solution:
fraction of original sample 500 g125 g
0.250 or14
x the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
14
, x 2
3.0 yrs 2 half-lifes, 1 half-life 1.5 yrs
PTS: 1 DIF: III REF: 2 OBJ: 3
SHORT ANSWER
20. ANS:
92235 U 2
4 He + 90231 Th
PTS: 1 DIF: L2 REF: p. 800 OBJ: 25.2.1 21. ANS:
14 days
PTS: 1 DIF: L2 REF: p. 804 | p. 806 OBJ: 25.2.2
ID: C
4
22. ANS: 6 years
PTS: 1 DIF: L1 REF: p. 804 OBJ: 25.2.2 23. ANS:
23 days/3.8 days = approximately 6 half-lives have passed.73.9 g (0.5)^6 = 1.2 g remaining.
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
24. ANS: number of half-lives = 60 hours / 15 hours = 4
remaining = 25.0 12
4 1.563 g
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
25. ANS: 57,300 years ago
PTS: 1 DIF: L3 REF: p. 806 OBJ: 25.2.2 26. ANS:
0.375g3.00g
18 1
2
3
3 = number of half-lives (exponent of 1/2)
42 days / 3 half-lives = 14 days (the half-life time)
PTS: 1 DIF: L3 REF: p. 804 OBJ: 25.2.2
Name: ________________________ Class: ___________________ Date: __________ ID: D
1
Nuclear Honors Practice
Essay
1. After 252 days, a 12.0-g starting sample of the radioisotope scandium-46 contains only 1.5 g of the isotope. What is the half-life of scandium-46? Explain your reasoning.
2. Manganese-52 has a half-life of 6 days. If the amount of manganese-52 in a sample is 32 g, how much manganese-52 will remain after 24 days?
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
____ 3. According to the table below, if a rock contains 25% as much uranium-235 as rocks being formed today, how old is the rock?
Nuclide Half-Life (years)
carbon-14 5.71 103
potassium-40 1.26 109
radium-226 1.60 103
thorium-230 7.54 104
uranium-235 7.04 108
a. 3.55 108 years c. 2.84 109 yearsb. 1.41 109 years d. 7.04 108 years
____ 4. When radium-226 (atomic number 88) decays by emitting an alpha particle, it becomes ____.a. radon-222 c. polonium-222b. polonium-224 d. radium-222
____ 5. What is the half-life of an isotope if 125 g of a 500 g sample of the isotope remain after 3.0 years?a. 3.5 years c. 4.5 yearsb. 1.5 years d. 2.5 years
____ 6. Balance the following equation: 93239 Np ____ + 1
0 e
a. 94239 Pu c. 90
239 Th
b. 94238 Pu d. 92
239 U
____ 7. How many half-lives are required for three-fourths of the nuclei of one isotope in a sample to decay?a. 3 c. 2
b.32
d.34
____ 8. What particle does nickel-57 emit when it decays to cobalt-57? (Remember to evaluate atomic numbers)a. positron c. protonb. neutron d. alpha particle
Name: ________________________ ID: D
2
____ 9. What particle is needed to complete the following equation?
714 N + ____ 6
14 C + 11 H
a. 10 e c. 2
4 He
b. 01 n d. 1
0 e
____ 10. Balance the following equation: 92238 U+ ____ 92
239 U
a. 11H c. 0
1n
b. 24 He d. 1
0 e
____ 11. Balance the following equation: 49Be+ 2
4 He 612 C + ____
a. 10 e c. 2
4 He
b. 01n d. 1
1H
____ 12. Balance the following equation: 88226 Ra 86
222 Rn____
a. 24 He c. 0
1n
b. 10 e d. 1
1H
____ 13. Balance the following equation: 37Li+ ____ 2
4 He + 24 He
a. 10 e c. 2
4 He
b. 01n d. 1
1H
____ 14. To what element does polonium-208 (atomic number 84) decay when it emits an alpha particle?
a. 82210 Po c. 86
214 Rn
b. 82204 Pb d. 82
210 Pb
____ 15. What particle is needed to complete this nuclear reaction?
98251 Cf 96
247 Cm + _____
a. 10 e c. 2
4 He
b. 11 H d. 0
1 n
Short Answer
16. The concentration of carbon-14 in a piece of wood from an ancient burial mound indicates that ten half-lives of this radioisotope have passed. If the half-life (t 1 2 ) for carbon-14 is 5730 years, approximately how many
years ago did this sample of wood die?
17. If the half-life of a radioactive material is 6 years, how many years will it take for one half of the original amount of material to decay?
18. The radioisotope radon-222 has a half-life of 3.8 days. How much of a 73.9-g sample of radon-222 would be left after approximately 23 days?
19. After 56 days, 4 g of phosphorus-32 has decayed to 0.25 g. What is the half-life of phosphorus-32?
20. What is the half-life of phosphorus-32 if, after 42 days, 0.375 g remains from a 3.00-g starting sample?
Name: ________________________ ID: D
3
21. If the half-life of sodium-24 is 15 hours, how much remains from a 25.0-g sample after 60 hours?
22. Complete the following nuclear reaction:
92
_U 2
4He + _231 __
Problem
23. Write the nuclear equation for each of the following reactions. Refer to a periodic table.
a. the alpha decay of 88226 Ra
b. the beta decay of 1739 Cl
c. the positron emission of 1530 P
24. Calculate the mass defect and the binding energy/nucleon of the nuclide 815 O, which has a mass of
15.00306565 amu. The mass of a proton is 1.007 276 47 amu and the mass of a neutron is 1.008 664 90. One amu = 1.6605 10–27 kg and the speed of light is 3.00 108 m/s.
25. What is the half-life of an isotope if after 2.00 weeks you have 31.25 g remaining from a 250.0 g starting sample size?
26. Phosphorus-32 has a half-life of 14.3 days. How many milligrams of phosphorus-32 remain after 71.5 days if you start with 4.00 mg of the isotope?
ID: D
1
Nuclear Honors PracticeAnswer Section
ESSAY
1. ANS: One-eighth of the sample remains, so the isotope must have decayed through 3 half-lives. Three half-lives = 252 days, so one half-life = 252/3 days. Therefore, the half-life of scandium-46 is 84 days.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
2. ANS: 24 days is the equivalent of 4 half-life periods. 1/16 of the original sample remains. 1/16 of 32 g is 2 g. There are 2 grams remaining.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
MULTIPLE CHOICE
3. ANS: BSolution: x number of half-lives
25% 14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
2 half-lives 7.04 108 yrs
1 half-life 14.08 108 yrs 1.14 109 yrs
PTS: 1 DIF: III REF: 2 OBJ: 4 4. ANS: A PTS: 1 DIF: L2 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1 5. ANS: B
Solution:
fraction of original sample 500 g125 g
0.250 or14
x the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
14
, x 2
3.0 yrs 2 half-lifes, 1 half-life 1.5 yrs
PTS: 1 DIF: III REF: 2 OBJ: 3 6. ANS: A PTS: 1 DIF: II REF: 1
OBJ: 4
ID: D
2
7. ANS: CSolution: x number of half-lives
14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
PTS: 1 DIF: I REF: 2 OBJ: 3 8. ANS: A PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1 9. ANS: B PTS: 1 DIF: L3 REF: p. 803 | p. 804
OBJ: 25.2.1 10. ANS: C PTS: 1 DIF: II REF: 1
OBJ: 4 11. ANS: B PTS: 1 DIF: II REF: 1
OBJ: 4 12. ANS: A PTS: 1 DIF: II REF: 1
OBJ: 4 13. ANS: D PTS: 1 DIF: II REF: 1
OBJ: 4 14. ANS: B PTS: 1 DIF: L3 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1 15. ANS: C PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1
SHORT ANSWER
16. ANS: 57,300 years ago
PTS: 1 DIF: L3 REF: p. 806 OBJ: 25.2.2 17. ANS:
6 years
PTS: 1 DIF: L1 REF: p. 804 OBJ: 25.2.2 18. ANS:
23 days/3.8 days = approximately 6 half-lives have passed.73.9 g (0.5)^6 = 1.2 g remaining.
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
19. ANS: 14 days
PTS: 1 DIF: L2 REF: p. 804 | p. 806 OBJ: 25.2.2
ID: D
3
20. ANS: 0.375g3.00g
18 1
2
3
3 = number of half-lives (exponent of 1/2)
42 days / 3 half-lives = 14 days (the half-life time)
PTS: 1 DIF: L3 REF: p. 804 OBJ: 25.2.2 21. ANS:
number of half-lives = 60 hours / 15 hours = 4
remaining = 25.0 12
4 1.563 g
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
22. ANS:
92235 U 2
4 He + 90231 Th
PTS: 1 DIF: L2 REF: p. 800 OBJ: 25.2.1
PROBLEM
23. ANS:
a. 88226 Ra 2
4 He 86222 Rn
b. 1739 Cl 1
e e 1839 Ar
c. 1530 P 1
0 e 1530 Si
PTS: 1 DIF: II REF: 1 OBJ: 4 24. ANS:
mass defect = 8(mass of proton) + 7(mass of neutron) mass of nuclide= 8(1.007 276 47 amu) +7(1.008 664 90 amu) 15.00306565 amu= 8.05821176 amu + 7.0606543 amu 15.00306565 amu= 15.11886606 amu 15.00306565 amu
mass defect = 0.11580041 amubinding energy/nucleon = (0.11580041 amu)(1.6605 1027 kg/amu)(3 108) ( m/s)2/15 nucleons = 3.846e–021 J/nucleonbinding energy/nucleon = 3.846e–021 J/nucleon
PTS: 1 DIF: III REF: 1 OBJ: 1
ID: D
4
25. ANS: half-life = 4.67 daysSolution:
fraction of original 31.25 g250.0 g
0.125 or18
x = the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
18
, x 3
2.00 weeks 3 half-lives
2.00 weeks3 half-lives
0.667 weekshalf-life
7 daysweek
4.67 days
PTS: 1 DIF: III REF: 2 OBJ: 3 26. ANS:
0.125 mgSolution:
7.15 days 1 half-life14.3 days
5 half-lives
4.00 mg 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
5
0.125 mg
PTS: 1 DIF: III REF: 2 OBJ: 3
Name: ________________________ Class: ___________________ Date: __________ ID: E
1
Nuclear Honors Practice
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
____ 1. Balance the following equation: 93239 Np ____ + 1
0 e
a. 94238 Pu c. 94
239 Pu
b. 92239 U d. 90
239 Th
____ 2. How many half-lives are required for three-fourths of the nuclei of one isotope in a sample to decay?
a. 2 c.34
b.32
d. 3
____ 3. What particle does nickel-57 emit when it decays to cobalt-57? (Remember to evaluate atomic numbers)a. positron c. alpha particleb. neutron d. proton
____ 4. To what element does polonium-208 (atomic number 84) decay when it emits an alpha particle?
a. 82210 Po c. 86
214 Rn
b. 82204 Pb d. 82
210 Pb
____ 5. What is the half-life of an isotope if 125 g of a 500 g sample of the isotope remain after 3.0 years?a. 3.5 years c. 2.5 yearsb. 1.5 years d. 4.5 years
____ 6. Balance the following equation: 92238 U+ ____ 92
239 U
a. 24 He c. 1
1H
b. 10 e d. 0
1n
____ 7. What particle is needed to complete the following equation?
714 N + ____ 6
14 C + 11 H
a. 01 n c. 1
0 e
b. 10 e d. 2
4 He
____ 8. Balance the following equation: 49Be+ 2
4 He 612 C + ____
a. 24 He c. 1
0 e
b. 01n d. 1
1H
____ 9. What particle is needed to complete this nuclear reaction?
98251 Cf 96
247 Cm + _____
a. 24 He c. 1
0 e
b. 01 n d. 1
1 H
____ 10. When radium-226 (atomic number 88) decays by emitting an alpha particle, it becomes ____.a. radium-222 c. polonium-222b. polonium-224 d. radon-222
Name: ________________________ ID: E
2
____ 11. According to the table below, if a rock contains 25% as much uranium-235 as rocks being formed today, how old is the rock?
Nuclide Half-Life (years)
carbon-14 5.71 103
potassium-40 1.26 109
radium-226 1.60 103
thorium-230 7.54 104
uranium-235 7.04 108
a. 2.84 109 years c. 7.04 108 yearsb. 1.41 109 years d. 3.55 108 years
____ 12. Balance the following equation: 88226 Ra 86
222 Rn____
a. 11H c. 1
0 e
b. 24 He d. 0
1n
____ 13. Balance the following equation: 37Li+ ____ 2
4 He + 24 He
a. 11H c. 2
4 He
b. 10 e d. 0
1n
Short Answer
14. Complete the following nuclear reaction:
92
_U 2
4He + _231 __
15. If the half-life of sodium-24 is 15 hours, how much remains from a 25.0-g sample after 60 hours?
16. After 56 days, 4 g of phosphorus-32 has decayed to 0.25 g. What is the half-life of phosphorus-32?
17. The radioisotope radon-222 has a half-life of 3.8 days. How much of a 73.9-g sample of radon-222 would be left after approximately 23 days?
18. If the half-life of a radioactive material is 6 years, how many years will it take for one half of the original amount of material to decay?
19. The concentration of carbon-14 in a piece of wood from an ancient burial mound indicates that ten half-lives of this radioisotope have passed. If the half-life (t 1 2 ) for carbon-14 is 5730 years, approximately how many
years ago did this sample of wood die?
20. What is the half-life of phosphorus-32 if, after 42 days, 0.375 g remains from a 3.00-g starting sample?
Name: ________________________ ID: E
3
Problem
21. Calculate the mass defect and the binding energy/nucleon of the nuclide 815 O, which has a mass of
15.00306565 amu. The mass of a proton is 1.007 276 47 amu and the mass of a neutron is 1.008 664 90. One amu = 1.6605 10–27 kg and the speed of light is 3.00 108 m/s.
22. Write the nuclear equation for each of the following reactions. Refer to a periodic table.
a. the alpha decay of 88226 Ra
b. the beta decay of 1739 Cl
c. the positron emission of 1530 P
23. Phosphorus-32 has a half-life of 14.3 days. How many milligrams of phosphorus-32 remain after 71.5 days if you start with 4.00 mg of the isotope?
24. What is the half-life of an isotope if after 2.00 weeks you have 31.25 g remaining from a 250.0 g starting sample size?
Essay
25. Manganese-52 has a half-life of 6 days. If the amount of manganese-52 in a sample is 32 g, how much manganese-52 will remain after 24 days?
26. After 252 days, a 12.0-g starting sample of the radioisotope scandium-46 contains only 1.5 g of the isotope. What is the half-life of scandium-46? Explain your reasoning.
ID: E
1
Nuclear Honors PracticeAnswer Section
MULTIPLE CHOICE
1. ANS: C PTS: 1 DIF: II REF: 1OBJ: 4
2. ANS: ASolution: x number of half-lives
14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
PTS: 1 DIF: I REF: 2 OBJ: 3 3. ANS: A PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1 4. ANS: B PTS: 1 DIF: L3 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1 5. ANS: B
Solution:
fraction of original sample 500 g125 g
0.250 or14
x the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
14
, x 2
3.0 yrs 2 half-lifes, 1 half-life 1.5 yrs
PTS: 1 DIF: III REF: 2 OBJ: 3 6. ANS: D PTS: 1 DIF: II REF: 1
OBJ: 4 7. ANS: A PTS: 1 DIF: L3 REF: p. 803 | p. 804
OBJ: 25.2.1 8. ANS: B PTS: 1 DIF: II REF: 1
OBJ: 4 9. ANS: A PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1 10. ANS: D PTS: 1 DIF: L2 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1
ID: E
2
11. ANS: BSolution: x number of half-lives
25% 14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
2 half-lives 7.04 108 yrs
1 half-life 14.08 108 yrs 1.14 109 yrs
PTS: 1 DIF: III REF: 2 OBJ: 4 12. ANS: B PTS: 1 DIF: II REF: 1
OBJ: 4 13. ANS: A PTS: 1 DIF: II REF: 1
OBJ: 4
SHORT ANSWER
14. ANS:
92235 U 2
4 He + 90231 Th
PTS: 1 DIF: L2 REF: p. 800 OBJ: 25.2.1 15. ANS:
number of half-lives = 60 hours / 15 hours = 4
remaining = 25.0 12
4 1.563 g
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
16. ANS: 14 days
PTS: 1 DIF: L2 REF: p. 804 | p. 806 OBJ: 25.2.2
17. ANS: 23 days/3.8 days = approximately 6 half-lives have passed.73.9 g (0.5)^6 = 1.2 g remaining.
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
18. ANS: 6 years
PTS: 1 DIF: L1 REF: p. 804 OBJ: 25.2.2 19. ANS:
57,300 years ago
PTS: 1 DIF: L3 REF: p. 806 OBJ: 25.2.2
ID: E
3
20. ANS: 0.375g3.00g
18 1
2
3
3 = number of half-lives (exponent of 1/2)
42 days / 3 half-lives = 14 days (the half-life time)
PTS: 1 DIF: L3 REF: p. 804 OBJ: 25.2.2
PROBLEM
21. ANS: mass defect = 8(mass of proton) + 7(mass of neutron) mass of nuclide
= 8(1.007 276 47 amu) +7(1.008 664 90 amu) 15.00306565 amu= 8.05821176 amu + 7.0606543 amu 15.00306565 amu= 15.11886606 amu 15.00306565 amu
mass defect = 0.11580041 amubinding energy/nucleon = (0.11580041 amu)(1.6605 1027 kg/amu)(3 108) ( m/s)2/15 nucleons = 3.846e–021 J/nucleonbinding energy/nucleon = 3.846e–021 J/nucleon
PTS: 1 DIF: III REF: 1 OBJ: 1 22. ANS:
a. 88226 Ra 2
4 He 86222 Rn
b. 1739 Cl 1
e e 1839 Ar
c. 1530 P 1
0 e 1530 Si
PTS: 1 DIF: II REF: 1 OBJ: 4 23. ANS:
0.125 mgSolution:
7.15 days 1 half-life14.3 days
5 half-lives
4.00 mg 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
5
0.125 mg
PTS: 1 DIF: III REF: 2 OBJ: 3
ID: E
4
24. ANS: half-life = 4.67 daysSolution:
fraction of original 31.25 g250.0 g
0.125 or18
x = the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
18
, x 3
2.00 weeks 3 half-lives
2.00 weeks3 half-lives
0.667 weekshalf-life
7 daysweek
4.67 days
PTS: 1 DIF: III REF: 2 OBJ: 3
ESSAY
25. ANS: 24 days is the equivalent of 4 half-life periods. 1/16 of the original sample remains. 1/16 of 32 g is 2 g. There are 2 grams remaining.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
26. ANS: One-eighth of the sample remains, so the isotope must have decayed through 3 half-lives. Three half-lives = 252 days, so one half-life = 252/3 days. Therefore, the half-life of scandium-46 is 84 days.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
Name: ________________________ Class: ___________________ Date: __________ ID: F
1
Nuclear Honors Practice
Short Answer
1. Complete the following nuclear reaction:
92
_U 2
4He + _231 __
2. After 56 days, 4 g of phosphorus-32 has decayed to 0.25 g. What is the half-life of phosphorus-32?
3. If the half-life of sodium-24 is 15 hours, how much remains from a 25.0-g sample after 60 hours?
4. What is the half-life of phosphorus-32 if, after 42 days, 0.375 g remains from a 3.00-g starting sample?
5. The concentration of carbon-14 in a piece of wood from an ancient burial mound indicates that ten half-lives of this radioisotope have passed. If the half-life (t 1 2 ) for carbon-14 is 5730 years, approximately how many
years ago did this sample of wood die?
6. If the half-life of a radioactive material is 6 years, how many years will it take for one half of the original amount of material to decay?
7. The radioisotope radon-222 has a half-life of 3.8 days. How much of a 73.9-g sample of radon-222 would be left after approximately 23 days?
Problem
8. Phosphorus-32 has a half-life of 14.3 days. How many milligrams of phosphorus-32 remain after 71.5 days if you start with 4.00 mg of the isotope?
9. Write the nuclear equation for each of the following reactions. Refer to a periodic table.
a. the alpha decay of 88226 Ra
b. the beta decay of 1739 Cl
c. the positron emission of 1530 P
10. What is the half-life of an isotope if after 2.00 weeks you have 31.25 g remaining from a 250.0 g starting sample size?
11. Calculate the mass defect and the binding energy/nucleon of the nuclide 815 O, which has a mass of
15.00306565 amu. The mass of a proton is 1.007 276 47 amu and the mass of a neutron is 1.008 664 90. One amu = 1.6605 10–27 kg and the speed of light is 3.00 108 m/s.
Essay
12. After 252 days, a 12.0-g starting sample of the radioisotope scandium-46 contains only 1.5 g of the isotope. What is the half-life of scandium-46? Explain your reasoning.
13. Manganese-52 has a half-life of 6 days. If the amount of manganese-52 in a sample is 32 g, how much manganese-52 will remain after 24 days?
Name: ________________________ ID: F
2
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
____ 14. Balance the following equation: 92238 U+ ____ 92
239 U
a. 01n c. 1
0 e
b. 24 He d. 1
1H
____ 15. Balance the following equation: 88226 Ra 86
222 Rn____
a. 01n c. 1
0 e
b. 24 He d. 1
1H
____ 16. According to the table below, if a rock contains 25% as much uranium-235 as rocks being formed today, how old is the rock?
Nuclide Half-Life (years)
carbon-14 5.71 103
potassium-40 1.26 109
radium-226 1.60 103
thorium-230 7.54 104
uranium-235 7.04 108
a. 3.55 108 years c. 1.41 109 yearsb. 2.84 109 years d. 7.04 108 years
____ 17. What particle is needed to complete this nuclear reaction?
98251 Cf 96
247 Cm + _____
a. 11 H c. 1
0 e
b. 01 n d. 2
4 He
____ 18. What particle is needed to complete the following equation?
714 N + ____ 6
14 C + 11 H
a. 10 e c. 2
4 He
b. 10 e d. 0
1 n
____ 19. What particle does nickel-57 emit when it decays to cobalt-57? (Remember to evaluate atomic numbers)a. alpha particle c. positronb. proton d. neutron
____ 20. What is the half-life of an isotope if 125 g of a 500 g sample of the isotope remain after 3.0 years?a. 3.5 years c. 4.5 yearsb. 1.5 years d. 2.5 years
Name: ________________________ ID: F
3
____ 21. How many half-lives are required for three-fourths of the nuclei of one isotope in a sample to decay?a. 3 c. 2
b.34
d.32
____ 22. Balance the following equation: 37Li+ ____ 2
4 He + 24 He
a. 01n c. 1
0 e
b. 11H d. 2
4 He
____ 23. Balance the following equation: 93239 Np ____ + 1
0 e
a. 92239 U c. 94
238 Pu
b. 90239 Th d. 94
239 Pu
____ 24. When radium-226 (atomic number 88) decays by emitting an alpha particle, it becomes ____.a. radon-222 c. radium-222b. polonium-224 d. polonium-222
____ 25. Balance the following equation: 49Be+ 2
4 He 612 C + ____
a. 24 He c. 1
1H
b. 10 e d. 0
1n
____ 26. To what element does polonium-208 (atomic number 84) decay when it emits an alpha particle?
a. 86214 Rn c. 82
204 Pb
b. 82210 Po d. 82
210 Pb
ID: F
1
Nuclear Honors PracticeAnswer Section
SHORT ANSWER
1. ANS:
92235 U 2
4 He + 90231 Th
PTS: 1 DIF: L2 REF: p. 800 OBJ: 25.2.1 2. ANS:
14 days
PTS: 1 DIF: L2 REF: p. 804 | p. 806 OBJ: 25.2.2
3. ANS: number of half-lives = 60 hours / 15 hours = 4
remaining = 25.0 12
4 1.563 g
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
4. ANS: 0.375g3.00g
18 1
2
3
3 = number of half-lives (exponent of 1/2)
42 days / 3 half-lives = 14 days (the half-life time)
PTS: 1 DIF: L3 REF: p. 804 OBJ: 25.2.2 5. ANS:
57,300 years ago
PTS: 1 DIF: L3 REF: p. 806 OBJ: 25.2.2 6. ANS:
6 years
PTS: 1 DIF: L1 REF: p. 804 OBJ: 25.2.2 7. ANS:
23 days/3.8 days = approximately 6 half-lives have passed.73.9 g (0.5)^6 = 1.2 g remaining.
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
ID: F
2
PROBLEM
8. ANS: 0.125 mgSolution:
7.15 days 1 half-life14.3 days
5 half-lives
4.00 mg 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
5
0.125 mg
PTS: 1 DIF: III REF: 2 OBJ: 3 9. ANS:
a. 88226 Ra 2
4 He 86222 Rn
b. 1739 Cl 1
e e 1839 Ar
c. 1530 P 1
0 e 1530 Si
PTS: 1 DIF: II REF: 1 OBJ: 4 10. ANS:
half-life = 4.67 daysSolution:
fraction of original 31.25 g250.0 g
0.125 or18
x = the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
18
, x 3
2.00 weeks 3 half-lives
2.00 weeks3 half-lives
0.667 weekshalf-life
7 daysweek
4.67 days
PTS: 1 DIF: III REF: 2 OBJ: 3
ID: F
3
11. ANS: mass defect = 8(mass of proton) + 7(mass of neutron) mass of nuclide
= 8(1.007 276 47 amu) +7(1.008 664 90 amu) 15.00306565 amu= 8.05821176 amu + 7.0606543 amu 15.00306565 amu= 15.11886606 amu 15.00306565 amu
mass defect = 0.11580041 amubinding energy/nucleon = (0.11580041 amu)(1.6605 1027 kg/amu)(3 108) ( m/s)2/15 nucleons = 3.846e–021 J/nucleonbinding energy/nucleon = 3.846e–021 J/nucleon
PTS: 1 DIF: III REF: 1 OBJ: 1
ESSAY
12. ANS: One-eighth of the sample remains, so the isotope must have decayed through 3 half-lives. Three half-lives = 252 days, so one half-life = 252/3 days. Therefore, the half-life of scandium-46 is 84 days.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
13. ANS: 24 days is the equivalent of 4 half-life periods. 1/16 of the original sample remains. 1/16 of 32 g is 2 g. There are 2 grams remaining.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
MULTIPLE CHOICE
14. ANS: A PTS: 1 DIF: II REF: 1OBJ: 4
15. ANS: B PTS: 1 DIF: II REF: 1OBJ: 4
16. ANS: CSolution: x number of half-lives
25% 14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
2 half-lives 7.04 108 yrs
1 half-life 14.08 108 yrs 1.14 109 yrs
PTS: 1 DIF: III REF: 2 OBJ: 4 17. ANS: D PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1 18. ANS: D PTS: 1 DIF: L3 REF: p. 803 | p. 804
OBJ: 25.2.1
ID: F
4
19. ANS: C PTS: 1 DIF: L2 REF: p. 801OBJ: 25.2.1
20. ANS: BSolution:
fraction of original sample 500 g125 g
0.250 or14
x the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
14
, x 2
3.0 yrs 2 half-lifes, 1 half-life 1.5 yrs
PTS: 1 DIF: III REF: 2 OBJ: 3 21. ANS: C
Solution: x number of half-lives
14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
PTS: 1 DIF: I REF: 2 OBJ: 3 22. ANS: B PTS: 1 DIF: II REF: 1
OBJ: 4 23. ANS: D PTS: 1 DIF: II REF: 1
OBJ: 4 24. ANS: A PTS: 1 DIF: L2 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1 25. ANS: D PTS: 1 DIF: II REF: 1
OBJ: 4 26. ANS: C PTS: 1 DIF: L3 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1
Name: ________________________ Class: ___________________ Date: __________ ID: G
1
Nuclear Honors Practice
Problem
1. Write the nuclear equation for each of the following reactions. Refer to a periodic table.
a. the alpha decay of 88226 Ra
b. the beta decay of 1739 Cl
c. the positron emission of 1530 P
2. Calculate the mass defect and the binding energy/nucleon of the nuclide 815 O, which has a mass of
15.00306565 amu. The mass of a proton is 1.007 276 47 amu and the mass of a neutron is 1.008 664 90. One amu = 1.6605 10–27 kg and the speed of light is 3.00 108 m/s.
3. Phosphorus-32 has a half-life of 14.3 days. How many milligrams of phosphorus-32 remain after 71.5 days if you start with 4.00 mg of the isotope?
4. What is the half-life of an isotope if after 2.00 weeks you have 31.25 g remaining from a 250.0 g starting sample size?
Essay
5. Manganese-52 has a half-life of 6 days. If the amount of manganese-52 in a sample is 32 g, how much manganese-52 will remain after 24 days?
6. After 252 days, a 12.0-g starting sample of the radioisotope scandium-46 contains only 1.5 g of the isotope. What is the half-life of scandium-46? Explain your reasoning.
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
____ 7. Balance the following equation: 93239 Np ____ + 1
0 e
a. 92239 U c. 94
238 Pu
b. 90239 Th d. 94
239 Pu
____ 8. When radium-226 (atomic number 88) decays by emitting an alpha particle, it becomes ____.a. radium-222 c. polonium-224b. radon-222 d. polonium-222
____ 9. What is the half-life of an isotope if 125 g of a 500 g sample of the isotope remain after 3.0 years?a. 2.5 years c. 4.5 yearsb. 1.5 years d. 3.5 years
____ 10. What particle is needed to complete the following equation?
714 N + ____ 6
14 C + 11 H
a. 24 He c. 1
0 e
b. 10 e d. 0
1 n
Name: ________________________ ID: G
2
____ 11. What particle is needed to complete this nuclear reaction?
98251 Cf 96
247 Cm + _____
a. 01 n c. 1
0 e
b. 24 He d. 1
1 H
____ 12. Balance the following equation: 88226 Ra 86
222 Rn____
a. 11H c. 2
4 He
b. 10 e d. 0
1n
____ 13. Balance the following equation: 92238 U+ ____ 92
239 U
a. 01n c. 2
4 He
b. 11H d. 1
0 e
____ 14. What particle does nickel-57 emit when it decays to cobalt-57? (Remember to evaluate atomic numbers)a. positron c. protonb. alpha particle d. neutron
____ 15. How many half-lives are required for three-fourths of the nuclei of one isotope in a sample to decay?
a.34
c. 3
b. 2 d.32
____ 16. Balance the following equation: 37Li+ ____ 2
4 He + 24 He
a. 01n c. 1
0 e
b. 24 He d. 1
1H
____ 17. To what element does polonium-208 (atomic number 84) decay when it emits an alpha particle?
a. 82204 Pb c. 82
210 Pb
b. 86214 Rn d. 82
210 Po
____ 18. According to the table below, if a rock contains 25% as much uranium-235 as rocks being formed today, how old is the rock?
Nuclide Half-Life (years)
carbon-14 5.71 103
potassium-40 1.26 109
radium-226 1.60 103
thorium-230 7.54 104
uranium-235 7.04 108
a. 2.84 109 years c. 1.41 109 yearsb. 7.04 108 years d. 3.55 108 years
Name: ________________________ ID: G
3
____ 19. Balance the following equation: 49Be+ 2
4 He 612 C + ____
a. 24 He c. 0
1n
b. 11H d. 1
0 e
Short Answer
20. Complete the following nuclear reaction:
92
_U 2
4He + _231 __
21. If the half-life of a radioactive material is 6 years, how many years will it take for one half of the original amount of material to decay?
22. If the half-life of sodium-24 is 15 hours, how much remains from a 25.0-g sample after 60 hours?
23. The radioisotope radon-222 has a half-life of 3.8 days. How much of a 73.9-g sample of radon-222 would be left after approximately 23 days?
24. After 56 days, 4 g of phosphorus-32 has decayed to 0.25 g. What is the half-life of phosphorus-32?
25. The concentration of carbon-14 in a piece of wood from an ancient burial mound indicates that ten half-lives of this radioisotope have passed. If the half-life (t 1 2 ) for carbon-14 is 5730 years, approximately how many
years ago did this sample of wood die?
26. What is the half-life of phosphorus-32 if, after 42 days, 0.375 g remains from a 3.00-g starting sample?
ID: G
1
Nuclear Honors PracticeAnswer Section
PROBLEM
1. ANS:
a. 88226 Ra 2
4 He 86222 Rn
b. 1739 Cl 1
e e 1839 Ar
c. 1530 P 1
0 e 1530 Si
PTS: 1 DIF: II REF: 1 OBJ: 4 2. ANS:
mass defect = 8(mass of proton) + 7(mass of neutron) mass of nuclide= 8(1.007 276 47 amu) +7(1.008 664 90 amu) 15.00306565 amu= 8.05821176 amu + 7.0606543 amu 15.00306565 amu= 15.11886606 amu 15.00306565 amu
mass defect = 0.11580041 amubinding energy/nucleon = (0.11580041 amu)(1.6605 1027 kg/amu)(3 108) ( m/s)2/15 nucleons = 3.846e–021 J/nucleonbinding energy/nucleon = 3.846e–021 J/nucleon
PTS: 1 DIF: III REF: 1 OBJ: 1 3. ANS:
0.125 mgSolution:
7.15 days 1 half-life14.3 days
5 half-lives
4.00 mg 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
5
0.125 mg
PTS: 1 DIF: III REF: 2 OBJ: 3
ID: G
2
4. ANS: half-life = 4.67 daysSolution:
fraction of original 31.25 g250.0 g
0.125 or18
x = the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
18
, x 3
2.00 weeks 3 half-lives
2.00 weeks3 half-lives
0.667 weekshalf-life
7 daysweek
4.67 days
PTS: 1 DIF: III REF: 2 OBJ: 3
ESSAY
5. ANS: 24 days is the equivalent of 4 half-life periods. 1/16 of the original sample remains. 1/16 of 32 g is 2 g. There are 2 grams remaining.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
6. ANS: One-eighth of the sample remains, so the isotope must have decayed through 3 half-lives. Three half-lives = 252 days, so one half-life = 252/3 days. Therefore, the half-life of scandium-46 is 84 days.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
MULTIPLE CHOICE
7. ANS: D PTS: 1 DIF: II REF: 1OBJ: 4
8. ANS: B PTS: 1 DIF: L2 REF: p. 800 | p. 804OBJ: 25.1.2 | 25.2.1
ID: G
3
9. ANS: BSolution:
fraction of original sample 500 g125 g
0.250 or14
x the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
14
, x 2
3.0 yrs 2 half-lifes, 1 half-life 1.5 yrs
PTS: 1 DIF: III REF: 2 OBJ: 3 10. ANS: D PTS: 1 DIF: L3 REF: p. 803 | p. 804
OBJ: 25.2.1 11. ANS: B PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1 12. ANS: C PTS: 1 DIF: II REF: 1
OBJ: 4 13. ANS: A PTS: 1 DIF: II REF: 1
OBJ: 4 14. ANS: A PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1 15. ANS: B
Solution: x number of half-lives
14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
PTS: 1 DIF: I REF: 2 OBJ: 3 16. ANS: D PTS: 1 DIF: II REF: 1
OBJ: 4 17. ANS: A PTS: 1 DIF: L3 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1 18. ANS: C
Solution: x number of half-lives
25% 14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
2 half-lives 7.04 108 yrs
1 half-life 14.08 108 yrs 1.14 109 yrs
PTS: 1 DIF: III REF: 2 OBJ: 4 19. ANS: C PTS: 1 DIF: II REF: 1
OBJ: 4
ID: G
4
SHORT ANSWER
20. ANS:
92235 U 2
4 He + 90231 Th
PTS: 1 DIF: L2 REF: p. 800 OBJ: 25.2.1 21. ANS:
6 years
PTS: 1 DIF: L1 REF: p. 804 OBJ: 25.2.2 22. ANS:
number of half-lives = 60 hours / 15 hours = 4
remaining = 25.0 12
4 1.563 g
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
23. ANS: 23 days/3.8 days = approximately 6 half-lives have passed.73.9 g (0.5)^6 = 1.2 g remaining.
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
24. ANS: 14 days
PTS: 1 DIF: L2 REF: p. 804 | p. 806 OBJ: 25.2.2
25. ANS: 57,300 years ago
PTS: 1 DIF: L3 REF: p. 806 OBJ: 25.2.2 26. ANS:
0.375g3.00g
18 1
2
3
3 = number of half-lives (exponent of 1/2)
42 days / 3 half-lives = 14 days (the half-life time)
PTS: 1 DIF: L3 REF: p. 804 OBJ: 25.2.2
Name: ________________________ Class: ___________________ Date: __________ ID: H
1
Nuclear Honors Practice
Essay
1. Manganese-52 has a half-life of 6 days. If the amount of manganese-52 in a sample is 32 g, how much manganese-52 will remain after 24 days?
2. After 252 days, a 12.0-g starting sample of the radioisotope scandium-46 contains only 1.5 g of the isotope. What is the half-life of scandium-46? Explain your reasoning.
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
____ 3. What is the half-life of an isotope if 125 g of a 500 g sample of the isotope remain after 3.0 years?a. 4.5 years c. 2.5 yearsb. 1.5 years d. 3.5 years
____ 4. How many half-lives are required for three-fourths of the nuclei of one isotope in a sample to decay?
a. 2 c.34
b. 3 d.32
____ 5. Balance the following equation: 49Be+ 2
4 He 612 C + ____
a. 11H c. 0
1n
b. 24 He d. 1
0 e
____ 6. What particle is needed to complete the following equation?
714 N + ____ 6
14 C + 11 H
a. 10 e c. 1
0 e
b. 24 He d. 0
1 n
____ 7. Balance the following equation: 37Li+ ____ 2
4 He + 24 He
a. 01n c. 1
1H
b. 10 e d. 2
4 He
____ 8. What particle is needed to complete this nuclear reaction?
98251 Cf 96
247 Cm + _____
a. 11 H c. 2
4 He
b. 01 n d. 1
0 e
____ 9. Balance the following equation: 92238 U+ ____ 92
239 U
a. 01n c. 1
0 e
b. 24 He d. 1
1H
Name: ________________________ ID: H
2
____ 10. When radium-226 (atomic number 88) decays by emitting an alpha particle, it becomes ____.a. radon-222 c. radium-222b. polonium-224 d. polonium-222
____ 11. Balance the following equation: 88226 Ra 86
222 Rn____
a. 11H c. 2
4 He
b. 01n d. 1
0 e
____ 12. Balance the following equation: 93239 Np ____ + 1
0 e
a. 92239 U c. 94
239 Pu
b. 94238 Pu d. 90
239 Th
____ 13. What particle does nickel-57 emit when it decays to cobalt-57? (Remember to evaluate atomic numbers)a. neutron c. alpha particleb. proton d. positron
____ 14. According to the table below, if a rock contains 25% as much uranium-235 as rocks being formed today, how old is the rock?
Nuclide Half-Life (years)
carbon-14 5.71 103
potassium-40 1.26 109
radium-226 1.60 103
thorium-230 7.54 104
uranium-235 7.04 108
a. 7.04 108 years c. 2.84 109 yearsb. 3.55 108 years d. 1.41 109 years
____ 15. To what element does polonium-208 (atomic number 84) decay when it emits an alpha particle?
a. 82204 Pb c. 82
210 Pb
b. 82210 Po d. 86
214 Rn
Short Answer
16. If the half-life of sodium-24 is 15 hours, how much remains from a 25.0-g sample after 60 hours?
17. If the half-life of a radioactive material is 6 years, how many years will it take for one half of the original amount of material to decay?
18. Complete the following nuclear reaction:
92
_U 2
4He + _231 __
19. The radioisotope radon-222 has a half-life of 3.8 days. How much of a 73.9-g sample of radon-222 would be left after approximately 23 days?
20. After 56 days, 4 g of phosphorus-32 has decayed to 0.25 g. What is the half-life of phosphorus-32?
Name: ________________________ ID: H
3
21. The concentration of carbon-14 in a piece of wood from an ancient burial mound indicates that ten half-lives of this radioisotope have passed. If the half-life (t 1 2 ) for carbon-14 is 5730 years, approximately how many
years ago did this sample of wood die?
22. What is the half-life of phosphorus-32 if, after 42 days, 0.375 g remains from a 3.00-g starting sample?
Problem
23. Calculate the mass defect and the binding energy/nucleon of the nuclide 815 O, which has a mass of
15.00306565 amu. The mass of a proton is 1.007 276 47 amu and the mass of a neutron is 1.008 664 90. One amu = 1.6605 10–27 kg and the speed of light is 3.00 108 m/s.
24. What is the half-life of an isotope if after 2.00 weeks you have 31.25 g remaining from a 250.0 g starting sample size?
25. Write the nuclear equation for each of the following reactions. Refer to a periodic table.
a. the alpha decay of 88226 Ra
b. the beta decay of 1739 Cl
c. the positron emission of 1530 P
26. Phosphorus-32 has a half-life of 14.3 days. How many milligrams of phosphorus-32 remain after 71.5 days if you start with 4.00 mg of the isotope?
ID: H
1
Nuclear Honors PracticeAnswer Section
ESSAY
1. ANS: 24 days is the equivalent of 4 half-life periods. 1/16 of the original sample remains. 1/16 of 32 g is 2 g. There are 2 grams remaining.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
2. ANS: One-eighth of the sample remains, so the isotope must have decayed through 3 half-lives. Three half-lives = 252 days, so one half-life = 252/3 days. Therefore, the half-life of scandium-46 is 84 days.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
MULTIPLE CHOICE
3. ANS: BSolution:
fraction of original sample 500 g125 g
0.250 or14
x the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
14
, x 2
3.0 yrs 2 half-lifes, 1 half-life 1.5 yrs
PTS: 1 DIF: III REF: 2 OBJ: 3 4. ANS: A
Solution: x number of half-lives
14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
PTS: 1 DIF: I REF: 2 OBJ: 3 5. ANS: C PTS: 1 DIF: II REF: 1
OBJ: 4 6. ANS: D PTS: 1 DIF: L3 REF: p. 803 | p. 804
OBJ: 25.2.1 7. ANS: C PTS: 1 DIF: II REF: 1
OBJ: 4
ID: H
2
8. ANS: C PTS: 1 DIF: L2 REF: p. 801OBJ: 25.2.1
9. ANS: A PTS: 1 DIF: II REF: 1OBJ: 4
10. ANS: A PTS: 1 DIF: L2 REF: p. 800 | p. 804OBJ: 25.1.2 | 25.2.1
11. ANS: C PTS: 1 DIF: II REF: 1OBJ: 4
12. ANS: C PTS: 1 DIF: II REF: 1OBJ: 4
13. ANS: D PTS: 1 DIF: L2 REF: p. 801OBJ: 25.2.1
14. ANS: DSolution: x number of half-lives
25% 14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
2 half-lives 7.04 108 yrs
1 half-life 14.08 108 yrs 1.14 109 yrs
PTS: 1 DIF: III REF: 2 OBJ: 4 15. ANS: A PTS: 1 DIF: L3 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1
SHORT ANSWER
16. ANS: number of half-lives = 60 hours / 15 hours = 4
remaining = 25.0 12
4 1.563 g
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
17. ANS: 6 years
PTS: 1 DIF: L1 REF: p. 804 OBJ: 25.2.2 18. ANS:
92235 U 2
4 He + 90231 Th
PTS: 1 DIF: L2 REF: p. 800 OBJ: 25.2.1
ID: H
3
19. ANS: 23 days/3.8 days = approximately 6 half-lives have passed.73.9 g (0.5)^6 = 1.2 g remaining.
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
20. ANS: 14 days
PTS: 1 DIF: L2 REF: p. 804 | p. 806 OBJ: 25.2.2
21. ANS: 57,300 years ago
PTS: 1 DIF: L3 REF: p. 806 OBJ: 25.2.2 22. ANS:
0.375g3.00g
18 1
2
3
3 = number of half-lives (exponent of 1/2)
42 days / 3 half-lives = 14 days (the half-life time)
PTS: 1 DIF: L3 REF: p. 804 OBJ: 25.2.2
PROBLEM
23. ANS: mass defect = 8(mass of proton) + 7(mass of neutron) mass of nuclide
= 8(1.007 276 47 amu) +7(1.008 664 90 amu) 15.00306565 amu= 8.05821176 amu + 7.0606543 amu 15.00306565 amu= 15.11886606 amu 15.00306565 amu
mass defect = 0.11580041 amubinding energy/nucleon = (0.11580041 amu)(1.6605 1027 kg/amu)(3 108) ( m/s)2/15 nucleons = 3.846e–021 J/nucleonbinding energy/nucleon = 3.846e–021 J/nucleon
PTS: 1 DIF: III REF: 1 OBJ: 1
ID: H
4
24. ANS: half-life = 4.67 daysSolution:
fraction of original 31.25 g250.0 g
0.125 or18
x = the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
18
, x 3
2.00 weeks 3 half-lives
2.00 weeks3 half-lives
0.667 weekshalf-life
7 daysweek
4.67 days
PTS: 1 DIF: III REF: 2 OBJ: 3 25. ANS:
a. 88226 Ra 2
4 He 86222 Rn
b. 1739 Cl 1
e e 1839 Ar
c. 1530 P 1
0 e 1530 Si
PTS: 1 DIF: II REF: 1 OBJ: 4 26. ANS:
0.125 mgSolution:
7.15 days 1 half-life14.3 days
5 half-lives
4.00 mg 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
5
0.125 mg
PTS: 1 DIF: III REF: 2 OBJ: 3
Name: ________________________ Class: ___________________ Date: __________ ID: I
1
Nuclear Honors Practice
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
____ 1. Balance the following equation: 92238 U+ ____ 92
239 U
a. 01n c. 2
4 He
b. 10 e d. 1
1H
____ 2. What is the half-life of an isotope if 125 g of a 500 g sample of the isotope remain after 3.0 years?a. 4.5 years c. 2.5 yearsb. 3.5 years d. 1.5 years
____ 3. When radium-226 (atomic number 88) decays by emitting an alpha particle, it becomes ____.a. radon-222 c. polonium-224b. radium-222 d. polonium-222
____ 4. What particle is needed to complete the following equation?
714 N + ____ 6
14 C + 11 H
a. 10 e c. 1
0 e
b. 01 n d. 2
4 He
____ 5. What particle does nickel-57 emit when it decays to cobalt-57? (Remember to evaluate atomic numbers)a. positron c. neutronb. proton d. alpha particle
____ 6. Balance the following equation: 93239 Np ____ + 1
0 e
a. 92239 U c. 90
239 Th
b. 94238 Pu d. 94
239 Pu
____ 7. Balance the following equation: 37Li+ ____ 2
4 He + 24 He
a. 11H c. 1
0 e
b. 24 He d. 0
1n
____ 8. How many half-lives are required for three-fourths of the nuclei of one isotope in a sample to decay?
a.34
c. 3
b.32
d. 2
____ 9. Balance the following equation: 49Be+ 2
4 He 612 C + ____
a. 01n c. 2
4 He
b. 10 e d. 1
1H
____ 10. Balance the following equation: 88226 Ra 86
222 Rn____
a. 10 e c. 2
4 He
b. 01n d. 1
1H
Name: ________________________ ID: I
2
____ 11. What particle is needed to complete this nuclear reaction?
98251 Cf 96
247 Cm + _____
a. 11 H c. 2
4 He
b. 01 n d. 1
0 e
____ 12. According to the table below, if a rock contains 25% as much uranium-235 as rocks being formed today, how old is the rock?
Nuclide Half-Life (years)
carbon-14 5.71 103
potassium-40 1.26 109
radium-226 1.60 103
thorium-230 7.54 104
uranium-235 7.04 108
a. 3.55 108 years c. 1.41 109 yearsb. 2.84 109 years d. 7.04 108 years
____ 13. To what element does polonium-208 (atomic number 84) decay when it emits an alpha particle?
a. 82210 Po c. 82
210 Pb
b. 82204 Pb d. 86
214 Rn
Short Answer
14. The radioisotope radon-222 has a half-life of 3.8 days. How much of a 73.9-g sample of radon-222 would be left after approximately 23 days?
15. If the half-life of sodium-24 is 15 hours, how much remains from a 25.0-g sample after 60 hours?
16. What is the half-life of phosphorus-32 if, after 42 days, 0.375 g remains from a 3.00-g starting sample?
17. After 56 days, 4 g of phosphorus-32 has decayed to 0.25 g. What is the half-life of phosphorus-32?
18. Complete the following nuclear reaction:
92
_U 2
4He + _231 __
19. If the half-life of a radioactive material is 6 years, how many years will it take for one half of the original amount of material to decay?
20. The concentration of carbon-14 in a piece of wood from an ancient burial mound indicates that ten half-lives of this radioisotope have passed. If the half-life (t 1 2 ) for carbon-14 is 5730 years, approximately how many
years ago did this sample of wood die?
Problem
21. Phosphorus-32 has a half-life of 14.3 days. How many milligrams of phosphorus-32 remain after 71.5 days if you start with 4.00 mg of the isotope?
Name: ________________________ ID: I
3
22. Calculate the mass defect and the binding energy/nucleon of the nuclide 815 O, which has a mass of
15.00306565 amu. The mass of a proton is 1.007 276 47 amu and the mass of a neutron is 1.008 664 90. One amu = 1.6605 10–27 kg and the speed of light is 3.00 108 m/s.
23. What is the half-life of an isotope if after 2.00 weeks you have 31.25 g remaining from a 250.0 g starting sample size?
24. Write the nuclear equation for each of the following reactions. Refer to a periodic table.
a. the alpha decay of 88226 Ra
b. the beta decay of 1739 Cl
c. the positron emission of 1530 P
Essay
25. After 252 days, a 12.0-g starting sample of the radioisotope scandium-46 contains only 1.5 g of the isotope. What is the half-life of scandium-46? Explain your reasoning.
26. Manganese-52 has a half-life of 6 days. If the amount of manganese-52 in a sample is 32 g, how much manganese-52 will remain after 24 days?
ID: I
1
Nuclear Honors PracticeAnswer Section
MULTIPLE CHOICE
1. ANS: A PTS: 1 DIF: II REF: 1OBJ: 4
2. ANS: DSolution:
fraction of original sample 500 g125 g
0.250 or14
x the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
14
, x 2
3.0 yrs 2 half-lifes, 1 half-life 1.5 yrs
PTS: 1 DIF: III REF: 2 OBJ: 3 3. ANS: A PTS: 1 DIF: L2 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1 4. ANS: B PTS: 1 DIF: L3 REF: p. 803 | p. 804
OBJ: 25.2.1 5. ANS: A PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1 6. ANS: D PTS: 1 DIF: II REF: 1
OBJ: 4 7. ANS: A PTS: 1 DIF: II REF: 1
OBJ: 4 8. ANS: D
Solution: x number of half-lives
14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
PTS: 1 DIF: I REF: 2 OBJ: 3 9. ANS: A PTS: 1 DIF: II REF: 1
OBJ: 4 10. ANS: C PTS: 1 DIF: II REF: 1
OBJ: 4 11. ANS: C PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1
ID: I
2
12. ANS: CSolution: x number of half-lives
25% 14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
2 half-lives 7.04 108 yrs
1 half-life 14.08 108 yrs 1.14 109 yrs
PTS: 1 DIF: III REF: 2 OBJ: 4 13. ANS: B PTS: 1 DIF: L3 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1
SHORT ANSWER
14. ANS: 23 days/3.8 days = approximately 6 half-lives have passed.73.9 g (0.5)^6 = 1.2 g remaining.
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
15. ANS: number of half-lives = 60 hours / 15 hours = 4
remaining = 25.0 12
4 1.563 g
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
16. ANS: 0.375g3.00g
18 1
2
3
3 = number of half-lives (exponent of 1/2)
42 days / 3 half-lives = 14 days (the half-life time)
PTS: 1 DIF: L3 REF: p. 804 OBJ: 25.2.2 17. ANS:
14 days
PTS: 1 DIF: L2 REF: p. 804 | p. 806 OBJ: 25.2.2
18. ANS:
92235 U 2
4 He + 90231 Th
PTS: 1 DIF: L2 REF: p. 800 OBJ: 25.2.1
ID: I
3
19. ANS: 6 years
PTS: 1 DIF: L1 REF: p. 804 OBJ: 25.2.2 20. ANS:
57,300 years ago
PTS: 1 DIF: L3 REF: p. 806 OBJ: 25.2.2
PROBLEM
21. ANS: 0.125 mgSolution:
7.15 days 1 half-life14.3 days
5 half-lives
4.00 mg 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
5
0.125 mg
PTS: 1 DIF: III REF: 2 OBJ: 3 22. ANS:
mass defect = 8(mass of proton) + 7(mass of neutron) mass of nuclide= 8(1.007 276 47 amu) +7(1.008 664 90 amu) 15.00306565 amu= 8.05821176 amu + 7.0606543 amu 15.00306565 amu= 15.11886606 amu 15.00306565 amu
mass defect = 0.11580041 amubinding energy/nucleon = (0.11580041 amu)(1.6605 1027 kg/amu)(3 108) ( m/s)2/15 nucleons = 3.846e–021 J/nucleonbinding energy/nucleon = 3.846e–021 J/nucleon
PTS: 1 DIF: III REF: 1 OBJ: 1
ID: I
4
23. ANS: half-life = 4.67 daysSolution:
fraction of original 31.25 g250.0 g
0.125 or18
x = the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
18
, x 3
2.00 weeks 3 half-lives
2.00 weeks3 half-lives
0.667 weekshalf-life
7 daysweek
4.67 days
PTS: 1 DIF: III REF: 2 OBJ: 3 24. ANS:
a. 88226 Ra 2
4 He 86222 Rn
b. 1739 Cl 1
e e 1839 Ar
c. 1530 P 1
0 e 1530 Si
PTS: 1 DIF: II REF: 1 OBJ: 4
ESSAY
25. ANS: One-eighth of the sample remains, so the isotope must have decayed through 3 half-lives. Three half-lives = 252 days, so one half-life = 252/3 days. Therefore, the half-life of scandium-46 is 84 days.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
26. ANS: 24 days is the equivalent of 4 half-life periods. 1/16 of the original sample remains. 1/16 of 32 g is 2 g. There are 2 grams remaining.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
Name: ________________________ Class: ___________________ Date: __________ ID: J
1
Nuclear Honors Practice
Short Answer
1. The radioisotope radon-222 has a half-life of 3.8 days. How much of a 73.9-g sample of radon-222 would be left after approximately 23 days?
2. If the half-life of a radioactive material is 6 years, how many years will it take for one half of the original amount of material to decay?
3. What is the half-life of phosphorus-32 if, after 42 days, 0.375 g remains from a 3.00-g starting sample?
4. Complete the following nuclear reaction:
92
_U 2
4He + _231 __
5. The concentration of carbon-14 in a piece of wood from an ancient burial mound indicates that ten half-lives of this radioisotope have passed. If the half-life (t 1 2 ) for carbon-14 is 5730 years, approximately how many
years ago did this sample of wood die?
6. After 56 days, 4 g of phosphorus-32 has decayed to 0.25 g. What is the half-life of phosphorus-32?
7. If the half-life of sodium-24 is 15 hours, how much remains from a 25.0-g sample after 60 hours?
Problem
8. Phosphorus-32 has a half-life of 14.3 days. How many milligrams of phosphorus-32 remain after 71.5 days if you start with 4.00 mg of the isotope?
9. What is the half-life of an isotope if after 2.00 weeks you have 31.25 g remaining from a 250.0 g starting sample size?
10. Calculate the mass defect and the binding energy/nucleon of the nuclide 815 O, which has a mass of
15.00306565 amu. The mass of a proton is 1.007 276 47 amu and the mass of a neutron is 1.008 664 90. One amu = 1.6605 10–27 kg and the speed of light is 3.00 108 m/s.
11. Write the nuclear equation for each of the following reactions. Refer to a periodic table.
a. the alpha decay of 88226 Ra
b. the beta decay of 1739 Cl
c. the positron emission of 1530 P
Essay
12. After 252 days, a 12.0-g starting sample of the radioisotope scandium-46 contains only 1.5 g of the isotope. What is the half-life of scandium-46? Explain your reasoning.
13. Manganese-52 has a half-life of 6 days. If the amount of manganese-52 in a sample is 32 g, how much manganese-52 will remain after 24 days?
Name: ________________________ ID: J
2
Multiple ChoiceIdentify the choice that best completes the statement or answers the question.
____ 14. Balance the following equation: 37Li+ ____ 2
4 He + 24 He
a. 11H c. 1
0 e
b. 24 He d. 0
1n
____ 15. Balance the following equation: 93239 Np ____ + 1
0 e
a. 90239 Th c. 94
239 Pu
b. 94238 Pu d. 92
239 U
____ 16. According to the table below, if a rock contains 25% as much uranium-235 as rocks being formed today, how old is the rock?
Nuclide Half-Life (years)
carbon-14 5.71 103
potassium-40 1.26 109
radium-226 1.60 103
thorium-230 7.54 104
uranium-235 7.04 108
a. 7.04 108 years c. 3.55 108 yearsb. 1.41 109 years d. 2.84 109 years
____ 17. Balance the following equation: 92238 U+ ____ 92
239 U
a. 10 e c. 0
1n
b. 24 He d. 1
1H
____ 18. What particle is needed to complete this nuclear reaction?
98251 Cf 96
247 Cm + _____
a. 24 He c. 0
1 n
b. 11 H d. 1
0 e
____ 19. What is the half-life of an isotope if 125 g of a 500 g sample of the isotope remain after 3.0 years?a. 2.5 years c. 3.5 yearsb. 1.5 years d. 4.5 years
____ 20. How many half-lives are required for three-fourths of the nuclei of one isotope in a sample to decay?a. 3 c. 2
b.32
d.34
Name: ________________________ ID: J
3
____ 21. What particle is needed to complete the following equation?
714 N + ____ 6
14 C + 11 H
a. 24 He c. 0
1 n
b. 10 e d. 1
0 e
____ 22. When radium-226 (atomic number 88) decays by emitting an alpha particle, it becomes ____.a. radon-222 c. polonium-222b. radium-222 d. polonium-224
____ 23. What particle does nickel-57 emit when it decays to cobalt-57? (Remember to evaluate atomic numbers)a. alpha particle c. neutronb. proton d. positron
____ 24. To what element does polonium-208 (atomic number 84) decay when it emits an alpha particle?
a. 82210 Po c. 82
210 Pb
b. 82204 Pb d. 86
214 Rn
____ 25. Balance the following equation: 88226 Ra 86
222 Rn____
a. 01n c. 2
4 He
b. 11H d. 1
0 e
____ 26. Balance the following equation: 49Be+ 2
4 He 612 C + ____
a. 24 He c. 0
1n
b. 10 e d. 1
1H
ID: J
1
Nuclear Honors PracticeAnswer Section
SHORT ANSWER
1. ANS: 23 days/3.8 days = approximately 6 half-lives have passed.73.9 g (0.5)^6 = 1.2 g remaining.
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
2. ANS: 6 years
PTS: 1 DIF: L1 REF: p. 804 OBJ: 25.2.2 3. ANS:
0.375g3.00g
18 1
2
3
3 = number of half-lives (exponent of 1/2)
42 days / 3 half-lives = 14 days (the half-life time)
PTS: 1 DIF: L3 REF: p. 804 OBJ: 25.2.2 4. ANS:
92235 U 2
4 He + 90231 Th
PTS: 1 DIF: L2 REF: p. 800 OBJ: 25.2.1 5. ANS:
57,300 years ago
PTS: 1 DIF: L3 REF: p. 806 OBJ: 25.2.2 6. ANS:
14 days
PTS: 1 DIF: L2 REF: p. 804 | p. 806 OBJ: 25.2.2
7. ANS: number of half-lives = 60 hours / 15 hours = 4
remaining = 25.0 12
4 1.563 g
PTS: 1 DIF: L3 REF: p. 804 | p. 805 OBJ: 25.2.2
ID: J
2
PROBLEM
8. ANS: 0.125 mgSolution:
7.15 days 1 half-life14.3 days
5 half-lives
4.00 mg 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
5
0.125 mg
PTS: 1 DIF: III REF: 2 OBJ: 3 9. ANS:
half-life = 4.67 daysSolution:
fraction of original 31.25 g250.0 g
0.125 or18
x = the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
18
, x 3
2.00 weeks 3 half-lives
2.00 weeks3 half-lives
0.667 weekshalf-life
7 daysweek
4.67 days
PTS: 1 DIF: III REF: 2 OBJ: 3 10. ANS:
mass defect = 8(mass of proton) + 7(mass of neutron) mass of nuclide= 8(1.007 276 47 amu) +7(1.008 664 90 amu) 15.00306565 amu= 8.05821176 amu + 7.0606543 amu 15.00306565 amu= 15.11886606 amu 15.00306565 amu
mass defect = 0.11580041 amubinding energy/nucleon = (0.11580041 amu)(1.6605 1027 kg/amu)(3 108) ( m/s)2/15 nucleons = 3.846e–021 J/nucleonbinding energy/nucleon = 3.846e–021 J/nucleon
PTS: 1 DIF: III REF: 1 OBJ: 1
ID: J
3
11. ANS:
a. 88226 Ra 2
4 He 86222 Rn
b. 1739 Cl 1
e e 1839 Ar
c. 1530 P 1
0 e 1530 Si
PTS: 1 DIF: II REF: 1 OBJ: 4
ESSAY
12. ANS: One-eighth of the sample remains, so the isotope must have decayed through 3 half-lives. Three half-lives = 252 days, so one half-life = 252/3 days. Therefore, the half-life of scandium-46 is 84 days.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
13. ANS: 24 days is the equivalent of 4 half-life periods. 1/16 of the original sample remains. 1/16 of 32 g is 2 g. There are 2 grams remaining.
PTS: 1 DIF: L2 REF: p. 804 | p. 805 OBJ: 25.2.2
MULTIPLE CHOICE
14. ANS: A PTS: 1 DIF: II REF: 1OBJ: 4
15. ANS: C PTS: 1 DIF: II REF: 1OBJ: 4
16. ANS: BSolution: x number of half-lives
25% 14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
2 half-lives 7.04 108 yrs
1 half-life 14.08 108 yrs 1.14 109 yrs
PTS: 1 DIF: III REF: 2 OBJ: 4 17. ANS: C PTS: 1 DIF: II REF: 1
OBJ: 4 18. ANS: A PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1
ID: J
4
19. ANS: BSolution:
fraction of original sample 500 g125 g
0.250 or14
x the number of half-lives
12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
14
, x 2
3.0 yrs 2 half-lifes, 1 half-life 1.5 yrs
PTS: 1 DIF: III REF: 2 OBJ: 3 20. ANS: C
Solution: x number of half-lives
14
(of original sample) 12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
x
,12
Ê
Ë
ÁÁÁÁÁÁ
ˆ
¯
˜̃̃˜̃̃
2
14
, thus x = 2 half-lives
PTS: 1 DIF: I REF: 2 OBJ: 3 21. ANS: C PTS: 1 DIF: L3 REF: p. 803 | p. 804
OBJ: 25.2.1 22. ANS: A PTS: 1 DIF: L2 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1 23. ANS: D PTS: 1 DIF: L2 REF: p. 801
OBJ: 25.2.1 24. ANS: B PTS: 1 DIF: L3 REF: p. 800 | p. 804
OBJ: 25.1.2 | 25.2.1 25. ANS: C PTS: 1 DIF: II REF: 1
OBJ: 4 26. ANS: C PTS: 1 DIF: II REF: 1
OBJ: 4
