Homework 10: Nuclear Chemistry

There are select solutions to these problems here.

Q10.1

Write the nuclear reaction for each process.

1. $$\ce{^{237}Np}$$ decays by α emission
2. $$\ce{^{240}U}$$ decays by β emission

Q10.1b

What nucleus is obtained in each process?

1. $$\ce{^{14}C}$$ decays by α emission
2. $$\ce{^{60}Co}$$ decays by β- emission.

Q10.2

Complete the following nuclear equations.

1. $$\mathrm{^{24}Mg + ? \rightarrow {^{25}Mg} + {^1H}}$$
2. $$\mathrm{^{103}Rh + {^1n} \rightarrow {^{93}Nb} + ?}$$
3. $$\mathrm{? + {^8Li} \rightarrow {^{207}Pb} + \beta}$$
4. $$\mathrm{^{208}Bi + ? \rightarrow {^{210}At} + 2^1n}$$

Q10.2b

Complete the nuclear equations:

1. $$\ce{^{231}Pa + ^2H \rightarrow ? + ^1H}$$
2. $$\ce{^{267}Rf + ^2H \rightarrow ^{269}Db + ?}$$
3. $$\ce{^9Be + ? \rightarrow ^{10}B + ^1n}$$
4. $$\ce{^{58}Fe + ^{227}Ac \rightarrow ?}$$
5. $$\ce{^{159}Tb + -1e \rightarrow ^{159}?}$$

Q10.3

Write the following nuclear equations:

1. the bombardment of $$\ce{^{14}N}$$ with protons to produce $$\ce{^{15}O}$$
2. bombardment of $$\ce{^{11}B}$$ with $$\ce{^2H}$$ to produce $$\ce{^{13}C}$$
3. bombardment of $$\ce{^{19}F}$$ with neutrons to produce $$\ce{^{21}F}$$

Q10.3b

Write out the following equations.

1. $$\ce{^{12}C}$$ is hit with $$\ce{^2H}$$ to produce $$\ce{^{14}N}$$
2. $$\ce{^{27}Al}$$ is hit with protons to produce $$\ce{^{28}Si}$$ and gamma rays
3. $$\ce{^7Li}$$ is hit with neutrons to produce $$\ce{^7He}$$

Q10.4

Write the nuclear equations to represent formation of isotope of element 105 with mass number 261 by bombardment of lead 207 with cobalt 59 followed by two alpha particle emissions.

Q10.4b

Write the equation for the nuclear reaction: the bombardment of $$\ce{^{73}Ge}$$ by $$\ce{^{108}Ag}$$ to form $$\ce{^{180}Au}$$ and followed by the bombardment of $$\ce{^{108}Ag}$$ with a neutron.

Q10.5

The $$\ce{^{14}C}$$ in a bone has a disintegration rate of 4000 dis h-1. The half life of $$\ce{^{14}C}$$ is 5730 years. Estimate the number of atoms of $$\ce{^{14}C}$$ is left in the bone.

Q10.5b

The disintegration rate for a sample containing $$\ce{^{60}Co}$$ as the only radioactive nuclide is 6800 dis h-1. Given that the half-life of $$\ce{^{60}Co}$$ is 5.5 years, estimate the number of atoms of $$\ce{^{60}Co}$$ in the sample.

10.6

Suppose the sample containing $$\ce{^{111}Ag}$$ has an activity of 500 times the detectable limit. How long would an experiment have to be run with this sample before the radioactivity could no longer be detected. The half life of $$\ce{^{111}Ag}$$ is 7.45 days.

Q10.6b

Suppose that a sample containing $$\ce{^{32}P}$$ has an activity 500 times the detectable limit. How long would an experiment have to run with this sample before the radioactivity could no longer be detected?

Q10.7

A wooden object is claimed to have been found in an ancient Chinese village and is offered for sale at an art museum. Radiocarbon dating of the object reveals a disintegration rate of 12 dis min-1 g-1. Is the object authentic? Why or why not?

Q10.7b

A fossil is found and is claimed to be of a baby dinosaur from the Mesozoic era. Radiocarbon dating of the fossil reveals a disintegration rate of 5.0 dismin-1g-1. Do you think the object is authentic? Explain.

Q10.8b

What should the mass ratio $$\ce{^{209}Bi/^{231}Pa}$$ in an object that is around 2.9X109 years old? The half life of $$\ce{^{231}Pa}$$ is 1.35X1011 years. [Hint: one $$\ce{^{209}Bi}$$ atom is final decay product of one $$\ce{^{231}Pa}$$ atom]

Q10.9

How much energy can be created from 1.2×10-22g of matter?

Q10.9b

Determine the energy associated with the destruction of 7.14 x 10-23 g of matter.

Q10.10

Calculate the energy, in mega electronvolt, released in the nuclear reaction. $$\mathrm{^{12}C + {^4He} \rightarrow {^{19}F} + {^1H}}$$

Q10.10b

Determine the energy released in the nuclear reaction, in megaelectronvolts   $$\ce{^{146}_{62}Sm \rightarrow ^{142}_{60}Nd + ^4_2He}$$.
Masses include: $$\mathrm{^{146}Sm= 145.913053\:u}$$
$$\mathrm{^{142}Nd= 141.907719\:u}$$
$$\mathrm{^4He= 4.002603\:u}$$

Q10.11

Which of the two species would be most abundant in nature?

1. $$\ce{^{16}O}$$ or $$\ce{^{18}O}$$
2. $$\ce{^{11}B}$$ or $$\ce{^{13}B}$$

Q11.11b

Which member of the following pairs of nuclides would you expect to be most abundant in natural sources?

1. $$\ce{^{15}N}$$  or  $$\ce{^{16}N}$$
2. $$\ce{^{12}C}$$  or  $$\ce{^{14}C}$$

Q10.12

Which of the two given species would be the most abundant in nature?

1. $$\ce{^{88}Sr}$$ or $$\ce{^{90}Sr}$$
2. $$\ce{^{28}Si}$$ or $$\ce{^{30}Si}$$
3. $$\ce{^{63}Ca}$$ or $$\ce{^{64}Ca}$$

Q10.12b

Which member of the following pairs of nuclides would you expect to be most abundant in natural sources?

1. $$\ce{^{14}C}$$ or $$\ce{^{13}C}$$
2. $$\ce{^{22}Na}$$ or $$\ce{^{23}Na}$$
3. $$\ce{^{13}N}$$ or $$\ce{^{14}N}$$

Q10.13

Balance each of the following nuclear equations and indicate the type of nuclear reaction ($$\alpha$$-emission, $$\beta$$-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. $$\mathrm{\ce{^{234}_{90}Th}\rightarrow {?}+\ce{^{234}_{91}?}}$$

Q10.14

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 $$\textrm{Cs-137}$$ remains in a sample of the isotope after 60 years?
3. What mass of $$\textrm{Cs}$$ will be left in a 24.0 g sample of $$\ce{^{137}_{55}Cs}$$ after 90 years?
4. What fraction of $$\textrm{Cs-137}$$ has decayed after 120 years?

Q10.15

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

Q10.16

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?

Q10.17

Write balanced nuclear equations for:

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

Q10.18

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

Q10.19

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

Q10.20

How much energy, in megaelectronvolts, is released in the following nuclear reaction?

$$\mathrm{\ce{^{241}_{95}Am} \rightarrow \ce{^{237}_{93}Np} + {^4_2He}}$$

The nuclidic masses are $$\mathrm{\ce{^{241}_{95}Am}=241.056829\, u}$$, $$\mathrm{\ce{^{237}_{93}Np}=237.0481734\, u}$$, and $$\mathrm{^4_2He=4.00260\, u}$$.

Q10.21

Calculate energy released in nuclear reaction:

$\mathrm{\ce{^{11}_6C} + {^4_2He} \rightarrow \ce{^{14}_7N} + {^1_1H}}$

given the following nuclear masses:

• $$\mathrm{\ce{^{11}_6C} = 10.9\,u}$$
• $$\mathrm{^4_2He = 3.21\,u}$$
• $$\mathrm{\ce{^{14}_7N} = 13.104\,u}$$
• $$\mathrm{^1_1H = 1.01\,u}$$

Q10.22

Which isotope is more likely to be the most abundant in nature? Explain.

1. $$\ce{^{32}_{18}Ar}$$ vs. $$\ce{^{52}_{18}Ar}$$
2. $$\ce{^{89}_{38}Sr}$$ vs. $$\ce{^{90}_{38}Sr}$$