# Homework 9: Nuclear Chemistry

There are select solutions to these problems here.

## Q9.5

Balance each of the following nuclear equations and indicate the type of nuclear reaction (a-emission, b-emission, fission, fusion, or “other”).

1. $$\mathrm{\ce{^{239}_{94}Pu}+\ce{^1_0n}\rightarrow \ce{^{130}_{50}Sn}+{?}+3^1_0n}$$
2. $$\mathrm{{?} + \ce{^{6}_{3}Li} \rightarrow 2^4_2He}$$
3. $$\mathrm{\ce{^{210}_{84}Po}\rightarrow \ce{^4_2He}}+{?}$$
4. $$\mathrm{\ce{^{235}_{92}U}+{^1_0n}\rightarrow \ce{^{72}_{30}?}+{?}+4^1_0n}$$
5. $$\mathrm{\ce{^{125}_{53}I}\rightarrow \ce{^{125}_{53}I}+{?}}$$
6. $$\mathrm{\ce{^{238}_{92}U}\rightarrow {?}+\ce{^{234}_{?}Th}}$$
7. $$\mathrm{\ce{^{235}_{92}U}+{^1_0n}\rightarrow \ce{^{86}_{?}Br}+\ce{^{147}_{?}?}+{?^1_0n}}$$
8. $$\mathrm{\ce{^{234}_{90}Th}\rightarrow {?}+\ce{^{234}_{91}?}}$$

## Q9.6

The isotope $$\ce{^{137}_{55}Cs}$$ undergoes beta emission with a half-life of 30 years.

1. Write a balanced nuclear equation for this reaction.
2. What fraction of Cs-137 remains in a sample of the isotope after 60 years?
3. What mass of Cs will be left in a 24.0 g sample of $$\ce{^{137}_{55}Cs}$$ after 90 years?
4. What fraction of Cs-137 has decayed after 120 years?

## Q9.7

What is the half-life of an isotope that is 75% decayed after 16 days?

## Q9.8

Explain what makes an isotope radioactive. Why do radioactive isotopes undergo radioactive decay? How does the energy released by nuclear reactions compare to that released by ordinary chemical reactions? Why?

## Q9.9

Write balanced nuclear equations for:

1. positron emission by Sr-83
2. the fusion of two C-12 nuclei to give another nucleus and a neutron.
3. the fission of U-235 to give Ba-140, another nucleus and an excess of two neutrons.

## Q9.10

What new element is formed when $$^{40}K$$ decays by $$\beta$$ emission? Is the new element formed likely to be stable? Why or why not?

## 9.11

Can is nuclear fission initiated a “chain reaction”? What is “critical” about critical mass? Why does nuclear fission produce radioactive waste?