Chapter 23 Worksheet 2

Predicting the type of radioactive decay

Why are some isotopes radioactive? (The belt of stability)

A better question is: “Why is any nucleus stable?” After all, except for hydrogen, all nuclei have multiple positive charges (protons) packed into a very small space (d ~ 10-4 angstroms). Why don’t they repel each other and fly apart? It must be that there is an attractive force between nucleons. This force, called the strong nuclear force, is only significant at very short distances (about the diameter of an average nucleus). The stability of nuclides depends on their neutron to proton ratio. Figure 20.2 (see last page of this handout) indicates the neutron to proton ratios for stable nuclei. The region which encompasses all the nonradioactive nuclides is called the “Belt of Stability.” Notice the ratio is about 1:1 for small nuclei but due to the short range of the strong nuclear force, larger nuclei need more neutrons to hold them together.

Predicting whether a nuclide is stable or radioactive

A nuclide of a given element will be radioactive if it:

has too many neutrons (high mass) → above the belt of stability

too few neutrons (low mass) → below the belt of stability

has an atomic number > 83 → beyond the belt of stability

Predicting the stability of a nuclide without reference to the belt of stability

We classify nuclei according to the “parity” of the neutron to proton ratio. For example,

is classified as even/odd since it has an even number of neutrons and an odd number of protons.

Nuclei with even numbers of protons and/or neutrons are more stable than those with odd numbers (see table 21.3 below) suggesting that proton pairs and neutron pairs have a special stability, analogous to pairs of electrons in molecules.

1. Nonradioactive nuclides always have at least as many neutrons as protons

(2 exceptions: 1H and 3He).

2. For an odd/even or even/odd nucleus, if the mass number of the nuclide differs by more than 1 amu

from the rounded atomic mass of the element taken from the periodic table, then the nuclide is

radioactive.

3. For an even/even nucleus, if the mass number of the nuclide is different by more than 3 amu from the

rounded atomic mass of the element taken from the periodic table, then the nuclide is radioactive.

4. For odd/odd nuclei only five isotopes are nonradioactive: 2H, 6Li, 10B, 14N, and 36Cl. All others are

radioactive.

5. All nuclides with Z>83 are radioactive.

Predicting the type of radioactivity

Unstable nuclei decay until they reach the belt of stability. The rules below are useful for predicting the type of radioactivity:

  1. Nuclei above the belt of stability (high neutron-to-proton ratios) usually emit -particles(one less neutron, one more proton!).
  2. Nuclei below the belt of stability (low neutron-to-proton ratios) either emit positrons or capture electrons(one more neutron, one less proton!).
  3. Nuclei with Z > 83 tend to undergo -decay (loses 2 protons and 2 neutrons; gets smaller fast!)

Some radioactive nuclei must undergo multiple steps to reach the belt of stability. An example is shown below.

Predicting the type of radioactivity without reference to “belt of stability”

1. If the mass number of a radioactive isotope is greater than the mass number found on the periodic table,

then the nuclide will decay by beta emission.

2. If the mass number of a radioactive isotope is less than the mass number found on the periodic table, then

the nuclide will either positron emit or electron capture (the latter is more likely for heavy nuclei).

3. Nuclides with Z>83 tend to alpha emit.

4. Predict whether the following nuclides are radioactive. If radioactive, predict how it would decay and write the balanced nuclear equation.

a)

b)

c)

d)

e)

f)

g)

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