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NUCLEAR CHEMISTRY
2F-1 (of 15)
NUCLEONS – The particles found in the nucleus
Protons (+)Neutrons (0)
ATOMIC NUMBER (Z) – The number of protons in the nucleus, also equal to the charge of the nucleus
MASS NUMBER (A) – The number of nucleons in the nucleus, or protons plus neutrons in the nucleus
and are isotopes
NUCLIDE – An atom with a specific number of protons and neutrons
ISOTOPES – A set of nuclides with the same number of protons
Hg80
196A Z
Protons: 80 Neutrons: 196 - 80 = 116
Hg80
196 Hg80
198
2F-2 (of 15)
NUCLEAR REACTIONS
Reactions that produce new atoms
TRANSMUTATION – When an atom of one element is changed into an atom of another element
14 N + 7
O + 17
8
Artificial elements are made by bombarding large nuclei with smaller ones
238 U +92
1 H 1
238 Np +93
He → 4
2
12 n 0
2 H → 1
2F-3 (of 15)
In all nuclear reactions (1) the mass number is conserved and (2) atomic number (or charge) is conserved
STABILITY SERIES
Nuclides are stable when their nuclei have enough neutrons to minimize proton-proton repulsion
(a) For Z < 20
Stable nuclei have n:p ratio of 1:1
(b) For Z > 20
As Z increases, stable nuclei have n:p ratio that increases from 1:1 to eventually 1.5:1
STABLE NUCLIDES (STABLE ISOTOPES) – Atoms with nuclei that last forever
RADIOACTIVE NUCLIDES (RADIOISOTOPES) – Atoms with nuclei that eventually break down to more stable nuclei
2F-4 (of 15)
Nuclides to the left of the line of stability are unstable because they are neutron poor
Nuclides to the right of the line of stability are unstable because they are neutron rich
Nuclides beyond the line of stability (with Z > 83) are unstable because they have too many total protons
Stable 16O atom:8 n, 8 p
(1:1 ratio)
Stable 200Hg atom:120 n, 80 p1.5:1 ratio
2F-5 (of 15)
Most of the stable nuclides have even numbers of protons and neutrons
Neutrons
Protons
Even Odd
Even
Odd
166
57
53
8
2F-6 (of 15)
There are 284 known stable nuclides
NUCLEAR DECAY – The process in which a radioactive nuclide turns into a more stable nuclide
The type of decay depends on whether the radioactive nuclide has too many total protons, if it is neutron rich, or if it is neutron poor
2F-7 (of 15)
α’s are emitted from radioisotopes beyond the line of stability, those with too many total protons (Z > 83 or A > 200)
(1) ALPHA DECAY (α) – The release of a helium-4 nucleus (4He2+) from a radioactive nucleus to become more stable
U →92
238 Th90
234 4 α +2
A and Z are always conserved in nuclear changes
Alpha particles can be stopped by the outermost layer of skin
2F-8 (of 15)
β-’s are emitted from radioisotopes that are to the right of the line of stability, those that are neutron rich
Essentially a neutron decays into a proton and an electron
(2) BETA MINUS DECAY (β-) – The release of an electron from a radioactive nucleus to become more stable
C → 6
14 N 7
14 0 β- +-1
Beta particles penetrate about 1 cm into the body
2F-9 (of 15)
EC occurs in radioisotopes to the left of the line of stability, those that are neutron poor
Essentially an electron and a proton turn into a neutron
(3) ELECTRON CAPTURE (EC) – An electron is captured by the nucleus to become more stable
Be + 4
7 Li 3
7 0 e- →-1
2F-10 (of 15)
β+’s are just like electrons, but with a positive charge
An electron is matter, but a β+ is ANTIMATTER
When a β+ and β- meet, they are ANNIHILATED, meaning all of their mass is converted into energy
A β+/β- annihilation forms 2 equal energy EM radiation photons
(4) POSITRON DECAY (β+) – The release of an electron with a positive charge from a nucleus to become more stable
2F-11 (of 15)
β+’s are emitted from radioisotopes to the left of the line of stability, those that are proton rich
Essentially a proton decays into a neutron and an antimatter electron
C → 6
11 B 5
11 0 β+ + 1
(4) POSITRON DECAY (β+) – The release of an electron with a positive charge from a nucleus to become more stable
2F-12 (of 15)
γ’s are emitted along with other forms of decay, or when an excited nucleus releases energy
(5) GAMMA DECAY (γ) – The release of any high energy photon of electromagnetic radiation
Ho → 67
163m Ho67
163 γ + 0
0
Gamma rays are deeply penetrating
2F-13 (of 15)
K →19
40 40 Ca20
0 β- +-1
+ γ 0
0
2F-14 (of 15)
Several neutrons, and lots of energy are released when nuclei fission
(6) SPONTANEOUS FISSION – When a large nucleus (Z > 80) breaks into two, approximately equal halves
U →92
239 Cd + 48
120 Ru +44
116 3 n 0
1
U →92
239 Ag + 47
119 Rh +45
118 2 n 0
1
Daughter Products
usually very radioactive, and always different
2F-15 (of 15)
THE RATE OF NUCLEAR DECAY
Each radioisotope undergoes nuclear decay at its own unique rate
HALF-LIFE (t1/2) – The time required for half of the radioisotopes in a sample to decay
The shorter the half-life, the more unstable the radioisotope
Half-life for 125I = 60 days
At 0 days:
At 60 days:
At 120 days:
At 180 days:
At 240 days:
16 125I atoms
8 125I atoms
4 125I atoms
2 125I atoms
1 125I atom
2G-1 (of 17)
Half-lives range from
1 x 10-21 seconds for 18Na
5 x 1015 years for 142Ce
Common half-lives
5,730 years for 14C
4.5 x 109 years for 238U
2G-2 (of 17)
THE DECAY EQUATION
n = n0e-kt
n0 = at time 0, number of atoms of a radioisotope (or g or disintegrations/time)
k = decay constant of a radioisotope (disintegrations atom-1 time-1)
t = time of decay
n = at time t, number of atoms of a radioisotope (or g or disintegrations/time)
2G-3 (of 17)
Half-life (t1/2) is the time needed so that ½ of n0 disintegrates
n0 = n0e-kt1/2
___
2
ln (1/2) = -kt1/2
ln 2 = t1/2
_____
k
1 = e-kt1/2
___
2
ln 2 = kt1/2
ln 2 = k _____
t1/2
or
n = n0e-kt
2G-4 (of 17)
THE DECAY EQUATION
n = n0e-kt n = n0e
- (ln2/t1/2)t
2G-5 (of 17)
Calculate the mass of 110Ag remaining after 2.00 minutes if you start with 1.00 g 110Ag and its half-life is 24 seconds.
= (1.00 g)e-(ln2/24 s)(120. s)
= 0.031 g
n = n0e-(ln2/t1/2)t
n and no can be anything proportional to the number of the radioactive atoms:
(1) grams, (2) moles, (3) disintegrations per time, (4) percentages, or of course (5) atoms
2G-6 (of 17)
Starting with 2.00 g of a radioisotope, after 1.00 hour only 0.63 g remain. Calculate the half-life.
n = n0e-(ln2/t1/2)t
n = e-(ln2/t1/2)t
___
n0
ln (n/n0) = -(ln2/t1/2)t
t1/2 =
-(ln2)t__________
ln (n/n0)
= 0.60 h = (ln2)t __________
ln (n0/n)
= (ln2)(1.00 h) _____________________
ln (2.00 g/0.63 g)
2G-7 (of 17)
CARBON DATING
In the atmosphere
14 N + 7
C + 14
6 n → 1
0 H 1
1
C + O2 → CO2 14
6
14 6
The carbon in all living organisms has the same percentage of 14C that the atmosphere has
15.3 dist. min-1 g-1 of carbon
When an organism dies, it stops taking in 14C, so the percentage starts dropping
2G-8 (of 17)
An axe with an elk antler sleve produces 4.8 cpm g-1 of carbon. How old is the axe?
n = n0e-(ln2/t1/2)t
n = e-(ln2/t1/2)t
___
n0
ln (n/n0) = -(ln2/t1/2)t
= 9,600 y t1/2 ln (n0/n) = t ______________
ln 2
= (5,730 y) ln (15.3 cpm g-1/4.8 cpm g-1) _______________________________________________
ln 2
2G-9 (of 17)
Much older objects can be dated with radioisotopes of longer half-lives
238U decays to 206Pb, so a material containing uranium can be dated by measuring the amount of 206Pb compared to 238U
2G-10 (of 17)
A rock weighing 4.267 g contains 1.023 g 238U and 0.112 g 206Pb. Calculate the age of the rock.
= 7.7 x 108 y t1/2 ln (n0/n) = t ______________
ln 2
= (4.5 x 109 y) ln (1.152 g/1.023 g) _______________________________________
ln 2
t1/2 = 4.5 x 109 y
n = 1.023 g
n0 = the original mass of 238U
0.112 g 206Pb
x mol 206Pb ______________
206 g 206Pb
x 1 mol 238U ______________
1 mol 206Pb
x 238 g 238U _____________
mol 238U
= 0.129 g + 1.023 g = 1.152 g
2G-11 (of 17)
STABILITY OF NUCLEI
Mass of proton + electron :
Mass of neutron :
1.007825 amu
1.008665 amu
Calculate the mass of a 23Na atom.
11 p+ + e-
12 n
= 11.086075 amu
= 12.103980 amu
11 x 1.007825 amu
12 x 1.008665 amu
= 23.190055 amu
Mass spectrometer data
Mass 23Na : 22.989773 amu
2G-12 (of 17)
23.190055 amu – 22.989773 amu = 0.200282 amu
BINDING ENERGY – The mass of an atom that has been converted into energy to hold the nucleus together
Through E = mc2 mass units can be converted into energy units
Mass loss of a 23Na atom:
1.000 amu = 1.492 x 10-10 J= 9.315 x 108 eV= 931.5 MeV
(Joule)(Electron Volt)(Million Electron Volt)
2G-13 (of 17)
0.200282 amu
x 931.5 MeV ______________
1.000 amu
= 186.6 MeV
This is the BINDING ENERGY of the 23Na nucleus
The stability of a nucleus is measured by its BINDING ENERGY PER NUCLEON
186.6 MeV________________
23 nucleons
= 8.113 MeV/nucleon
2G-14 (of 17)
Calculate the binding energy per nucleon for 56Fe if it has a mass of 55.934930 amu.
26 p+ + e-
30 n
= 26.203450 amu
= 30.259950 amu
26 x 1.007825 amu
30 x 1.008665 amu
= 56.463400 amu
56.463400 amu – 55.934930 amu = 0.528470 amu
x 1 _______________
56 nucleons
0.528470 amu
x 931.5 MeV ______________
1.000 amu
= 8.791 MeV/nucleon
2G-15 (of 17)
56Fe is the most stable atom
When large atoms break down they release energy
When small atoms combine they release energy
2G-16 (of 17)
FUSION – The combining of small nuclei to produce large nuclei
Fusion occurs in stars
4 H → 1
1 He 2
4
Very high temperatures or pressure are needed to overcome the repulsion of the positive hydrogen nuclei
Fusion releases much more energy than fission
Stars can fuse atoms to create even atomic numbered elements all the way up to 56Fe
2G-17 (of 17)
NUCLEAR REACTORS
235U is used as a fuel
U + 92
235 U92
236 n → 0
1
236U decays by spontaneous fission
CHAIN REACTION – When at least one neutron per fission produces a new 236U
Nuclear reactions release over 100 times more energy than chemical reactions
2G’-1 (of 4)
Not enough neutrons are
captured for a chain reaction
CRITICAL MASS – The minimum amount of 235U needed to support a chain reaction
Enough neutrons are captured to just maintain a chain reaction
So many neutrons are captured the chain reaction is
an explosion
2G’-2 (of 4)
Water – Acts as a MODERATOR to slow down the neutrons, as a COOLANT to keep the reactor core from overheating, and as PROTECTION because it absorbs radiation
Cd or B Control Rods – Absorb neutrons to control the rate of the chain reaction
Fuel Elements – Metal casings containing 235U
Reactor Core
2G’-3 (of 4)
San Onofre Nuclear Generating Station
Heat from the nuclear fission boils water, and steam turns a turbine, which produces electricity
Used up full elements contain radioactive daughter products, which must be disposed of safely
2G’-4 (of 4)
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