Chemistry

Educators

Problem 1

Write the following isotopes in hyphenated form (e.g." "carbon-14")
(a) 24
(b) 11
(b) 29
(c) $\frac{73}{13} \mathrm{Kr}$
(d) $\frac{73}{36} \mathrm{Kr}$
(d) $\frac{194}{77} \mathrm{Ir}$

Rikhil M.

Problem 2

Write the following isotopes in nuclide notation (e.g., $\stackrel{n 14}{6} \mathrm{C}^{\prime \prime} )$
(a) oxygen-14
(b) copper-70
(c) tantalum-175
(d) francium-217

Problem 3

For the following isotopes that have missing information, fill in the missing information to complete the
notation
(a) $\frac{34}{14} \mathrm{X}$
(b) $\quad \stackrel{36}{\mathrm{X}} \mathrm{P}$
(c) $\quad \mathrm{x}^{57} \mathrm{Mn}$
(d) $\frac{121}{56} \mathrm{X}$

Rikhil M.

Problem 4

For each of the isotopes in Exercise 21.1, determine the numbers of protons, neutrons, and electrons in a
neutral atom of the isotope.

Problem 5

Write the nuclide notation, including charge if applicable, for atoms with the following characteristics:
(a) 25 protons, 20 neutrons, 24 electrons
(b) 45 protons, 24 neutrons, 43 electrons
(c) 53 protons, 89 neutrons, 54 electrons
(d) 97 protons, 146 neutrons, 97 electrons

Rikhil M.

Problem 6

Calculate the density of the 24 Mg nucleus in $\mathrm{g} / \mathrm{mL}$ , assuming that the typical nuclear diameter of $1 \times$ $10^{-13} \mathrm{cm}$ and is spherical in shape.

Problem 7

What are the two principal differences between nuclear reactions and ordinary chemical changes?

Rikhil M.

Problem 8

The mass of the atom 11 $\mathrm{Na}$ is 22.9898 amu.
(a) Calculate its binding energy per atom in millions of electron volts.
(b) Calculate its binding energy per nucleon.

Problem 9

Which of the following nuclei lie within the band of stability shown in Figure 21.2$?$
(a) chlorine-37
(b) calcium- 40
(c) 204 $\mathrm{Bi}$
(d) 56 $\mathrm{Fe}$
(e) $^{206} \mathrm{Pe}$
(f) $^{211} \mathrm{P} \mathrm{b}$
(g) 222 $\mathrm{Rn}$
(h) carbon-14

Rikhil M.

Problem 10

Which of the following nuclei lie within the band of stability shown in Figure 21.2$?$
(a) argon-40
(b) oxygen-16
(c) $^{122} \mathrm{Ba}$
(d) $^{58} \mathrm{Ni}$
(e) $^{205} \mathrm{Tl}$
(f) $^{210} \mathrm{T} 1$
(g) 226 $\mathrm{Ra}$
(h) magnesium- 24

Problem 11

Write a brief description or definition of each of the following:
(a) nucleon
(b) $\alpha$ particle
(c) $\beta$ particle
(d) positron
(e) positron
(f) $\mathrm{Y}$ ray
(f) nuclide
(g) mass number
(g) atomic number

Rikhil M.

Problem 12

Which of the various particles (? particles, ? particles, and so on) that may be produced in a nuclear reaction are actually nuclei?

Problem 13

Complete each of the following equations by adding the missing species:
(a) $\frac{27}{13} \mathrm{Al}+_{2}^{4} \mathrm{He} \longrightarrow ?+_{0}^{1} \mathrm{n}$
(b) $239 \mathrm{Pu}+? \longrightarrow_{96}^{242} \mathrm{Cm}+_{0}^{1} \mathrm{n}$
(c) $14 \mathrm{N}+_{2}^{4} \mathrm{He} \longrightarrow ?+_{1}^{1} \mathrm{H}$
(d) $\frac{235}{92} \mathrm{U} \longrightarrow ?+\frac{135}{55} \mathrm{Cs}+4_{0}^{1} \mathrm{n}$

Rikhil M.

Problem 14

Complete each of the following equations:
(a) $\frac{7}{3} \mathrm{Li}+? \longrightarrow 2_{2}^{4} \mathrm{He}$
(b) $14 \mathrm{C} \longrightarrow^{14} \mathrm{N}+?$
(c) $27 \mathrm{Al}+_{2}^{4} \mathrm{He} \longrightarrow ?+_{0}^{1} \mathrm{n}$
(d) $_{96}^{250} \mathrm{Cm} \longrightarrow 2+_{38}^{98} \mathrm{Sr}+4_{0}^{1} \mathrm{n}$

Problem 15

Write a balanced equation for each of the following nuclear reactions:
(a) the production of 17 $\mathrm{O}$ from $^{14} \mathrm{N}$ by $\alpha$ particle bombardment
(b) the production of $^{14} \mathrm{C}$ from 14 $\mathrm{N}$ by neutron bombardment
(c) the production of $^{233}$ Th from $^{232}$ Th by neutron bombardment
(d) the production of 399 $\mathrm{U}$ from $^{238} \mathrm{U}$ by $_{1}^{2} \mathrm{H}$ bombardment

Rikhil M.

Problem 16

Technetium- 99 is prepared from $^{98}$ Molybdenum- 98 combines with a neutron to give molybdenum- $99,$ an unstable isotope that emits a ? particle to yield an excited form of technetium-99, represented as 99 $\mathrm{Tc}^{*} .$ This excited nucleus relaxes to the ground state, represented as $99 \mathrm{Tc},$ by emitting a y ray. The ground state of $^{99} \mathrm{Tc}$ then emits a $\beta$ particle. Write the equations for each of these nuclear reactions.

Problem 17

The mass of the atom $\quad \stackrel{19}{9} \mathrm{F}$ is 18.99840 amu.
(a) Calculate its binding energy per atom in millions of electron volts.
(b) Calculate its binding energy per nucleon.

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Problem 18

For the reaction $14 \mathrm{C} \longrightarrow \stackrel{14}{7} \mathrm{N}+?,$ if 100.0 $\mathrm{g}$ of carbon reacts, what volume of nitrogen gas $\left(\mathrm{N}_{2}\right)$ is produced at 273 $\mathrm{K}$ and 1 atm?

Problem 19

What are the types of radiation emitted by the nuclei of radioactive elements?

Rikhil M.

Problem 20

What changes occur to the atomic number and mass of a nucleus during each of the following decay scenarios?
(a) an $\alpha$ particle is emitted
(b) a $\beta$ particle is emitted
(c) $\mathrm{y}$ radiation is emitted
(d) a positron is emitted
(e) an electron is captured

Problem 21

What is the change in the nucleus that results from the following decay scenarios?
(a) emission of a $\beta$ particle
(b) emission of a $\beta^{+}$ particle
(c) capture of an electron

Rikhil M.

Problem 22

Many nuclides with atomic numbers greater than 83 decay by processes such as electron emission. Explain the observation that the emissions from these unstable nuclides also normally include ? particles.

Problem 23

Why is electron capture accompanied by the emission of an X-ray?

Rikhil M.

Problem 24

Explain, in terms of Figure 21.2, how unstable heavy nuclides (atomic number > 83) may decompose to form nuclides of greater stability (a) if they are below the band of stability and (b) if they are above the band of stability.

Problem 25

Which of the following nuclei is most likely to decay by positron emission? Explain your choice.
(a) chromium- 53
(b) manganese- 51
(c) iron- 59

Rikhil M.

Problem 26

The following nuclei do not lie in the band of stability. How would they be expected to decay? Explain your answer
(a) $\frac{34}{15} \mathrm{P}$
(b) $\frac{239}{92} \mathrm{U}$
(c) $\frac{38}{20} \mathrm{Ca}$
(d) 3 $\mathrm{H}$
(e) 245 $\mathrm{Pu}$

Problem 27

The following nuclei do not lie in the band of stability. How would they be expected to decay?
(a) 28 $\mathrm{P}$
(b) $\frac{235}{92} \mathrm{U}$
(c) 37 $\mathrm{Ca}$
(d) 9 $\mathrm{Li}$
(e) $\stackrel{245}{96} \mathrm{Cm}$

Rikhil M.

Problem 28

Predict by what mode(s) of spontaneous radioactive decay each of the following unstable isotopes might proceed:
(a) $_{2}^{6} \mathrm{He}$
(b) 60 $\mathrm{Zn}$
(c) $\frac{235}{91} \mathrm{Pa}$
(d) 241
(e) $^{18} \mathrm{F}$

Problem 29

Write a nuclear reaction for each step in the formation of $\frac{218}{84} \mathrm{Po}$ from $\frac{238}{98} \mathrm{U}$ which proceeds by a series of decay reactions involving the step-wise emission of $\alpha, \beta, \beta, \alpha, \alpha, \alpha$ particles, in that order.

Rikhil M.

Problem 30

Write a nuclear reaction for each step in the formation of 208 $\mathrm{Pb}$ from 2228 $\mathrm{Th}$ , which proceeds by a series of decay reactions involving the step-wise emission of $\alpha, \alpha, \alpha, \alpha, \beta, \beta, \alpha$ particles, in that order.

Problem 31

Define the term half-life and illustrate it with an example.

Rikhil M.

Problem 32

$\mathrm{A} 1.00 \times 10^{-6}-\mathrm{g}$ sample of nobelium, 254 $\mathrm{No}$ has a half-life of 55 seconds after it is formed. What is the percentage of $\frac{254}{102}$ No remaining at the following times?
(a) 5.0 min after it forms
(b) 1.0 $\mathrm{h}$ after it forms

Problem 33

239 $\mathrm{Pu}$ is a nuclear waste byproduct with a half-life of $24,000 \mathrm{y}$ . What fraction of the 239 Pu present today will be present in 1000 y?

Rikhil M.

Problem 34

The isotope 208 Tl undergoes $\beta$ decay with a half-life of 3.1 $\mathrm{min}$ .
(a) What isotope is produced by the decay?
(b) How long will it take for 99.0$\%$ of a sample of pure $^{208} \mathrm{T}$ to decay?
(c) What percentage of a sample of pure $^{208}$ Tl remains un-decayed after 1.0 $\mathrm{h} ?$

Problem 35

If 1.000 g of 226 Ra produces 0.0001 $\mathrm{mL}$ of the gas 222 $\mathrm{Rn}$ at STP (standard temperature and pressure) in 24 h, what is the half-life of 226 Ra in years?

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Problem 36

The isotope $\frac{\gamma_{0}}{38} \mathrm{Sr}$ is one of the extremely hazardous species in the residues from nuclear power generation. The strontium in a 0.500 -g sample diminishes to 0.393 $\mathrm{g}$ in 10.0 y. Calculate the half-life.

Problem 37

Technetium- 99 is often used for assessing heart, liver, and lung damage certain technetium compounds
are absorbed by damaged tissues. It has a half-life of 6.0 $\mathrm{h}$ . Calculate the rate constant for the decay of $\frac{99}{43} \mathrm{Tc}$

Rikhil M.

Problem 38

What is the age of mummified primate skin that contains 8.25$\%$ of the original quantity of $^{14} \mathrm{C} ?$

Problem 39

A sample of rock was found to contain 8.23 $\mathrm{mg}$ of rubidium- 87 and 0.47 $\mathrm{mg}$ of strontium- 87
(a) Calculate the age of the rock if the half-life of the decay of rubidium by $\beta$ emission is $4.7 \times 10^{10} \mathrm{y} .$
(b) If some $\frac{87}{38} \mathrm{Sr}$ was initially present in the rock, would the rock be younger, older, or the same age as the age calculated in $(\mathrm{a})$ ? Explain your answer.

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Problem 40

A laboratory investigation shows that a sample of uranium ore contains 5.37 $\mathrm{mg}$ of 238 $\mathrm{U}$ and 2.52 $\mathrm{mg}$ of $_{82}^{206} \mathrm{Pb}$ Calculate the age of the ore. The half-life of 238 $\mathrm{U}$ is $4.5 \times 10^{9} \mathrm{yr.}$

Problem 41

Plutonium was detected in trace amounts in natural uranium deposits by Glenn Seaborg and his associates in $1941 .$ They proposed that the source of this $^{239} \mathrm{Pu}$ was the capture of neutrons by $^{238} \mathrm{U}$ nuclei. Why is this plutonium not likely to have been trapped at the time the solar system formed $4.7 \times 10^{9}$ years ago?

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Problem 42

A $\frac{7}{4}$ Be atom (mass $=7.0169$ amu) decays into a $\frac{7}{3}$ Li atom (mass $=7.0160$ amu) by electron capture. How much energy (in millions of electron volts, MeV) is produced by this reaction?

Problem 43

$A_{5}^{8} B$ atom $(\operatorname{mas} s=8.0246 \text { amu) }$ decays into a $_{4}^{8} \mathrm{B}$ atom (mass $=8.0053$ amu) by loss of a $\beta^{4}$ particle (mass $=$ 0.00055 amu) or by electron capture. How much energy (in millions of electron volts) is produced by this reaction?

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Problem 44

Isotopes such as $^{26} \mathrm{Al}$ (half-life: $7.2 \times 10^{5}$ years) are believed to have been present in our solar system as it formed, but have since decayed and are now called extinct nuclides. .
(a) 26 Al decays by $\beta^{+}$ emission or electron capture. Write the equations for these two nuclear transformations.
(b) The earth was formed about $4.7 \times 10^{9}(4.7 \text { billion) years ago. How old was the earth when } 99.999999 \% \text { of the }$ 26 Al originally present had decayed?

Problem 45

Write a balanced equation for each of the following nuclear reactions:
(a) bismuth-212 decays into polonium- 212
(b) beryllium- 8 and a positron are produced by the decay of an unstable nucleus
(c) neptunium-239 forms from the reaction of uranium-238 with a neutron and then spontaneously converts into plutonium- $-239$
(d) strontium- 90 decays into yttrium-90

Rikhil M.

Problem 46

Write a balanced equation for each of the following nuclear reactions:
(a) mercury-180 decays into platinum-176
(b) zirconium $-90$ and an electron are produced by the decay of an unstable nucleus
(c) neptunium-239 forms from the reaction of uranium-238 with a neutron and then spontaneously converts into plutonium- 239
(d) neon-19 decays into fluorine- 19

Problem 47

Write the balanced nuclear equation for the production of the following transuranium elements:
(a) berkelium-244, made by the reaction of Am-241 and He-4
(b) fermium-254, made by the reaction of Pu-239 with a large number of neutrons
(c) lawrencium-257, made by the reaction of Cf-250 and B-11
(d) dubnium-260, made by the reaction of Cf-249 and N-15

Rikhil M.

Problem 48

How does nuclear fission differ from nuclear fusion? Why are both of these processes exothermic?

Problem 49

Both fusion and fission are nuclear reactions. Why is a very high temperature required for fusion, but not for fission?

Rikhil M.

Problem 50

Cite the conditions necessary for a nuclear chain reaction to take place. Explain how it can be controlled to produce energy, but not produce an explosion

Problem 51

Describe the components of a nuclear reactor.

Rikhil M.

Problem 52

In usual practice, both a moderator and control rods are necessary to operate a nuclear chain reaction safely for the purpose of energy production. Cite the function of each and explain why both are necessary.

Problem 53

Describe how the potential energy of uranium is converted into electrical energy in a nuclear power plant.

Rikhil M.

Problem 54

The mass of a hydrogen atom $\left(_{1}^{1} \mathrm{H}\right)$ is 1.007825 amu; that of a tritium atom $\left(\begin{array}{c}{3} \\ {1}\end{array}\right)$ is 3.01605 amu; and that of an a particle is 4.00150 amu. How much energy in killojoules per mole of $\frac{4}{2}$ He produced is released by the following fusion reaction: $1 \mathrm{H}+_{1}^{3} \mathrm{H} \longrightarrow_{2}^{4} \mathrm{He}$

Problem 55

How can a radioactive nuclide be used to show that the equilibrium:
$\mathrm{AgCl}(s) \rightleftharpoons \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q)$
is a dynamic equilibrium?

Rikhil M.

Problem 56

Technetium-99m has a half-life of 6.01 hours. If a patient injected with technetium-99m is safe to leave the hospital once 75% of the dose has decayed, when is the patient allowed to leave?

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Problem 57

Iodine that enters the body is stored in the thyroid gland from which it is released to control growth and
metabolism. The thyroid can be imaged if iodine-131 is injected into the body. In larger doses, I-133 is also used as a means of treating cancer of the thyroid. I-131 has a half-life of 8.70 days and decays by ?? emission.

Rikhil M.

Problem 58

If a hospital were storing radioisotopes, what is the minimum containment needed to protect against:
(a) cobalt-60 (a strong y emiter used for iradiation)
(b) molybdenum- 99 (a beta emitter used to produce technetium- 99 for imaging)

Problem 59

Based on what is known about Radon-2222's primary decay method, why is inhalation so dangerous?

Rikhil M.

Problem 60

Given specimens uranium-232 $\left(t_{12}=68.9 \mathrm{y}\right)$ and uranium-233 $\left(t_{1 / 2}=159,200 \mathrm{y}\right)$ of equal mass, which one would have greater activity and why?

Problem 61

A scientist is studying a 2.234 g sample of thorium-229 $\left(t_{1 / 2}=7340 \mathrm{y}\right)$ in a laboratory.
(a) What is its activity in Bq?
(b) What is its activity in Ci?

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Problem 62

Given specimens neon- 24$\left(t_{1 / 2}=3.38 \text { min) and bismuth-211 }\left(t_{1 / 2}=2.14 \text { min) of equal mass, which one would }\right.\right.$ have greater activity and why?