Physics for Scientists and Engineers, 6e

Chapter 44 - Nuclear Structure

Consider the following three nuclei: 12C, 13N, 14O. These nuclei have the same

1 2 3

33% 33%33%

1 2 3 4 5

1. number of protons

2. number of neutrons

3. number of nucleons

The value of N = A – Z is the same for all three nuclei.

Consider the following three nuclei: 12N, 13N, 14N. These nuclei have the same

1 2 3

33% 33%33%

1 2 3 4 5

1. number of protons

2. number of neutrons

3. number of nucleons

The value of Z is the same for all three nuclei because they are all nuclei of nitrogen.

Consider the following three nuclei: 14C, 14N, 14O. These nuclei have the same

1 2 3

33% 33%33%

1 2 3 4 5

1. number of protons

2. number of neutrons

3. number of nucleons

The value of A is the same for all three nuclei, as seen by the unchanging pre-superscript.

On your birthday, you measure the activity of a sample of 210Bi, which has a half-life of 5.01 days. The activity you measure is 1.000 μCi. What is the activity of this sample on your next birthday?

1 2 3 4 5

20% 20% 20%20%20%

1 2 3 4 5

1. 1.000 μCi

2. 0

3. ~ 0.2 μCi

4. ~ 0.01 μCi

5. ~ 10–22 μCi

A year of 365 days is equivalent to 365 d/5.01 d ≈ 73 half-lives. Thus, the activity will be reduced after one year to approximately (1/2)73 (1.000 μCi) ~ 10–22 μCi.

Suppose you have a pure radioactive material with a half-life of T1/2. You begin with N0 undecayed

nuclei of the material at t = 0. At 1/2t = T1/2, how

many of the nuclei have decayed?

1 2 3 4 5

20% 20% 20%20%20%

1 2 3 4 5

1. 1/4N0

2. 1/2N0

3. 3/4N0

4. 0.707N0

5. 0.293N0

The time we are interested in is half of a half-life. Thus, the number of remaining nuclei is (1/2)1/2N0 = N0 / √2 = 0.707N0. The number of

nuclei that have decayed is N0 – 0.707N0 =

0.293N0.

Which of the following is the correct daughter nucleus associated with the alpha decay of ?

1 2 3

33% 33%33%

1 2 3 4 5

1.

2.

3.

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

Which of the following is the correct daughter nucleus associated with the beta decay of ?

1 2 3

33% 33%33%

1 2 3 4 5

1.

2.

3.

In e– decay, the atomic number increases by one and the atomic mass number stays fixed. None of the choices is consistent with e+ decay, so we assume that the decay must be by e–.

Which of the following do you expect not to vary substantially mong different isotopes of an element?

1 2 3

33% 33%33%

1 2 3 4 5

1. atomic mass number

2. nuclear spin magnetic moment

3. chemical properties

Isotopes of a given element correspond to nuclei with different numbers of neutrons. This results in different atomic mass numbers of the nucleus—and different magnetic moments, because the neutron, despite being uncharged, has a magnetic moment. The chemical behavior, however, is governed by the electrons. All isotopes of a given element have the same number of electrons and, therefore, the same chemical behavior.