25.2 Nuclear Transformations > 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Nuclear Stability and Decay What determines

25.2 Nuclear Transformations >25.2 Nuclear Transformations >

1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved.

Nuclear Stability and Decay

What determines the type of decay a radioisotope

undergoes?



Nuclear Stability and Nuclear Stability and DecayDecay

A nucleus may be unstable and undergo spontaneous decay for different reasons.

The neutron-to-proton ratio in a radioisotope determines the type of decay that occurs.



The nuclear force is an attractive force that acts between all nuclear particles that are extremely close

together, such as protons and neutrons in a nucleus.

• At these short distances, the nuclear force dominates over electromagnetic repulsions and holds the nucleus together.



The stability of a nucleus depends on the ratio of neutrons to protons.

Interpret DataInterpret Data

• This graph shows the number of neutrons vs. the number of protons for all known stable nuclei.

Band of Stability.



Interpret DataInterpret Data

• For elements of low atomic number (below about 20), this ratio is about 1.

• Above atomic number 20, stable nuclei have more neutrons than protons.




Some nuclei are unstable because they have too many neutrons relative to the number of protons. • When one of these nuclei decays, a neutron

emits a beta particle (fast-moving electron) from the nucleus.

– A neutron that emits an electron becomes a proton.

n10 p +1

1 e 0–1

– This process is known as beta emission.

– It increases the number of protons while decreasing the number of neutrons.




Radioisotopes that undergo beta emission include the following.

Cu6629 Zn +66

30 e 0–1

C146 N +14

7 e 0–1




Other nuclei are unstable because they have too few neutrons relative to the number of protons.

• These nuclei increase their stability by converting a proton to a neutron.

– An electron is captured by the nucleus during this process, which is called electron capture.

Co

5927Ni + e59

280

–1

Cl 3717Ar + e37

180

–1




A positron is a particle with the mass of an electron but a positive charge.

• Its symbol is e.

• During positron emission, a proton changes to a neutron, just as in electron capture.

0+1

B85 Be +8

4 e 0+1

O158 N +15

7 e 0+1

– the atomic number decreases by 1 and the number of neutrons increases by 1.




Nuclei that have an atomic number greater than 83 are radioactive.

• These nuclei have both too many neutrons and too many protons to be stable.– Therefore, they undergo radioactive decay.

– Alpha emission increases the neutron-to-proton ratio, which tends to increase the stability of the nucleus.

• Most of them emit alpha particles.




In alpha emission, the mass number decreases by four and the atomic number decreases by two.

Ra22688 Rn + He222

8642

Th23290 Ra + He228

8842




Recall that conservation of mass is an important property of chemical reactions.

• In contrast, mass is not conserved during nuclear reactions.

• An extremely small quantity of mass is converted into energy released during radioactive decay.



During nuclear decay, if the atomic number decreases by one but the mass number is unchanged, the radiation emitted is

A. a positron.

B. an alpha particle.

C. a beta particle.

D. a proton.



During nuclear decay, if the atomic number decreases by one but the mass number is unchanged, the radiation emitted is

A. a positron.

B. an alpha particle.

C. a beta particle.

D. a proton.



Half-Life

How much of a radioactive sample remains after each half-

life?

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Half-LifeHalf-LifeSection 15.4 & Screen 15.8Section 15.4 & Screen 15.8

•HALF-LIFEHALF-LIFE is the time it takes for 1/2 a is the time it takes for 1/2 a sample is disappear.sample is disappear.

• The rate of a nuclear transformation depends The rate of a nuclear transformation depends only on the “reactant” concentration.only on the “reactant” concentration.

• Concept of HALF-LIFE is especially useful for Concept of HALF-LIFE is especially useful for 1st order reactions.1st order reactions.

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Half-LifeHalf-Life

Decay of 20.0 mg of Decay of 20.0 mg of 1515O. What remains after 3 O. What remains after 3 half-lives? After 5 half-lives?half-lives? After 5 half-lives?



A half-life (t ) is the time required for one-half of the nuclei in a radioisotope sample to decay to products.

12

Interpret GraphsInterpret Graphs

After each half-life, half of the original radioactive atoms have decayed into atoms of a new element.



Half-lives can be as short as a second or as long as billions of years.

Half-Lives of Some Naturally Occurring Radioisotopes

Isotope Half-life Radiation emitted

Carbon-14 5.73 × 103 years

Potassium-40 1.25 × 109 years

Radon-222 3.8 days

Radium-226 1.6 × 103 years

Thorium-234 24.1 days

Uranium-235 7.0 × 108 years

Uranium-238 4.5 × 109 years

Comparing Half-Lives



Half-LifeHalf-Life

• Scientists use half-lives of some long-term radioisotopes to determine the age of ancient objects.

• Many artificially produced radioisotopes have short half-lives, which makes them useful in nuclear medicine.

– Short-lived isotopes are not a long-term radiation hazard for patients.

Comparing Half-Lives



Half-LifeHalf-LifeComparing Half-Lives

• The age of uranium-containing minerals can be estimated by measuring the ratio of uranium-238 to lead-206.

• Because the half-life of uranium-238 is 4.5 × 109

years, it is possible to use its half-life to date rocks as old as the solar system.

Uranium-238 decays through a complex series of unstable isotopes to the stable isotope lead-206.



Half-LifeHalf-LifeRadiocarbon Dating

Plants use carbon dioxide to produce carbon compounds, such as glucose.

• The ratio of carbon-14 to other carbon isotopes is constant during an organism’s life.

• When an organism dies, it stops exchanging carbon with the environment and its radioactive C atoms decay without being replaced.

• Archaeologists can use this data to estimate when an organism died.

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Half-LifeHalf-Life

Exponential Decay Function

• A stands for the amount remaining.

• A0 stands for the initial amount.

• n stands for the number of half-lives.

You can use the following equation to calculate how much of an isotope will remain after a given number of half-lives.

A = A0 12

n



Half-LifeHalf-Life

• The exponent n indicates how many times A0 must be multiplied by to determine A.

12

A = A0 12

n

Exponential Decay Function



Using Half-Lives in Calculations

Sample Problem 25.1Sample Problem 25.1

Carbon-14 emits beta radiation and decays with a half-life (t ) of 5730 years. Assume that you start with a mass of 2.00 × 10–12 g of carbon-14.

12

a. How long is three half-lives?

b. How many grams of the isotope remain at the end of three half-lives?



KNOWNS UNKNOWNS3 half-lives = ? years

mass remaining = ? g

Analyze List the knowns and the unknowns.1


• To calculate the length of three half-lives, multiply the half-life by three.

• To find the mass of the radioisotope remaining, multiply the original mass by for each half-life that has elapsed.

12

t = 5730 years

initial mass (A0) = 2.00 × 10–12 g

number of half-lives (n) = 3

12



a. Multiply the half-life of carbon-14 by the total number of half-lives.

Calculate Solve for the unknowns.2


t × n = 5730 years × 3 = 17,190 years12





b. The initial mass of carbon-14 is reduced by one-half for each half-life. So, multiply by three times.1

2

Remaining mass = 2.00 × 10–12 g × × ×12

12

12

= 0.250 × 10–12 g

= 2.50 × 10–13 g





b. You can get the same answer by using the equation for an exponential decay function.

= (2.00 × 10–12 g)

= 0.250 × 10–12 g

= 2.50 × 10–13 g

A = A0 = (2.00 × 10–12 g) ( )12

n ( )12

3

( )18



The half-life of phosphorus-32 is 14.3 days. How many milligrams of phosphorus-32 remain after 100.1 days if you begin with 2.5 mg of the radioisotope?



The half-life of phosphorus-32 is 14.3 days. How many milligrams of phosphorus-32 remain after 100.1 days if you begin with 2.5 mg of the radioisotope?

n = 100.1 days × = 7 half-lives 1 half-life14.3 days

= (2.5 mg) = 2.0 × 10–2 mg

A = A0 = (2.5 mg) ( )12

n ( )12

7

( ) 1128



Which of the following always changes when transmutation occurs?

A. The number of electrons

B. The mass number

C. The atomic number

D. The number of neutrons

C. The atomic number



Key EquationKey Equation

A = A0 12

n

34Kinetics of Radioactive Kinetics of Radioactive DecayDecay

Activity (A) = Disintegrations/time Activity

(A) = (k)(N)

where N is the number of atoms

Decay is first order, and so

ln (A/Ao) = -kt

The half-life of

radioactive decay is t1/2 = 0.693/k

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25.2 Nuclear Transformations > 1 Copyright © Pearson Education, Inc., or its affiliates. All Rights Reserved. Nuclear Stability and Decay What determines