nuclear chemistry homework answers

(a) sodium-24; (b) aluminum-29; (c) krypton-73; (d) iridium-194

(a) 14 34 Si ; 14 34 Si ; (b) 15 36 P ; 15 36 P ; (c) 25 57 Mn ; 25 57 Mn ; (d) 56 121 Ba 56 121 Ba

(a) 25 45 Mn +1 ; 25 45 Mn +1 ; (b) 45 69 Rh +2 ; 45 69 Rh +2 ; (c) 53 142 I −1 ; 53 142 I −1 ; (d) 97 243 Bk 97 243 Bk

Nuclear reactions usually change one type of nucleus into another; chemical changes rearrange atoms. Nuclear reactions involve much larger energies than chemical reactions and have measureable mass changes.

(a), (b), (c), (d), and (e)

(a) A nucleon is any particle contained in the nucleus of the atom, so it can refer to protons and neutrons. (b) An α particle is one product of natural radioactivity and is the nucleus of a helium atom. (c) A β particle is a product of natural radioactivity and is a high-speed electron. (d) A positron is a particle with the same mass as an electron but with a positive charge. (e) Gamma rays compose electromagnetic radiation of high energy and short wavelength. (f) Nuclide is a term used when referring to a single type of nucleus. (g) The mass number is the sum of the number of protons and the number of neutrons in an element. (h) The atomic number is the number of protons in the nucleus of an element.

(a) 13 27 Al + 2 4 He ⟶ 15 30 P + 0 1 n ; 13 27 Al + 2 4 He ⟶ 15 30 P + 0 1 n ; (b) 94 239 Pu + 2 4 He ⟶ 96 242 Cm + 0 1 n ; 94 239 Pu + 2 4 He ⟶ 96 242 Cm + 0 1 n ; (c) 7 14 N + 2 4 He ⟶ 8 17 O + 1 1 H ; 7 14 N + 2 4 He ⟶ 8 17 O + 1 1 H ; (d) 92 235 U ⟶ 37 96 Rb + 55 135 Cs + 4 0 1 n 92 235 U ⟶ 37 96 Rb + 55 135 Cs + 4 0 1 n

(a) 7 14 N + 2 4 He ⟶ 8 17 O + 1 1 H ; 7 14 N + 2 4 He ⟶ 8 17 O + 1 1 H ; (b) 7 14 C + 0 1 n ⟶ 6 14 C + 1 1 H ; 7 14 C + 0 1 n ⟶ 6 14 C + 1 1 H ; (c) 90 232 Th + 0 1 n ⟶ 90 233 Th ; 90 232 Th + 0 1 n ⟶ 90 233 Th ; (d) 1 92 238 U + 1 2 H ⟶ 92 239 U + 1 1 H 1 92 238 U + 1 2 H ⟶ 92 239 U + 1 1 H

(a) 148.8 MeV per atom; (b) 7.808 MeV/nucleon

α (helium nuclei), β (electrons), β + (positrons), and η (neutrons) may be emitted from a radioactive element, all of which are particles; γ rays also may be emitted.

(a) conversion of a neutron to a proton: 0 1 n ⟶ 1 1 p + +1 0 e ; 0 1 n ⟶ 1 1 p + +1 0 e ; (b) conversion of a proton to a neutron; the positron has the same mass as an electron and the same magnitude of positive charge as the electron has negative charge; when the n:p ratio of a nucleus is too low, a proton is converted into a neutron with the emission of a positron: 1 1 p ⟶ 0 1 n + +1 0 e ; 1 1 p ⟶ 0 1 n + +1 0 e ; (c) In a proton-rich nucleus, an inner atomic electron can be absorbed. In simplest form, this changes a proton into a neutron: 1 1 p + -1 0 e ⟶ 0 1 p 1 1 p + -1 0 e ⟶ 0 1 p

The electron pulled into the nucleus was most likely found in the 1 s orbital. As an electron falls from a higher energy level to replace it, the difference in the energy of the replacement electron in its two energy levels is given off as an X-ray.

Manganese-51 is most likely to decay by positron emission. The n:p ratio for Cr-53 is 29 24 29 24 = 1.21; for Mn-51, it is 26 25 26 25 = 1.04; for Fe-59, it is 33 26 33 26 = 1.27. Positron decay occurs when the n:p ratio is low. Mn-51 has the lowest n:p ratio and therefore is most likely to decay by positron emission. Besides, 24 53 Cr 24 53 Cr is a stable isotope, and 26 59 Fe 26 59 Fe decays by beta emission.

(a) β decay; (b) α decay; (c) positron emission; (d) β decay; (e) α decay

92 238 U ⟶ 90 234 Th + 2 4 He ; 92 238 U ⟶ 90 234 Th + 2 4 He ; 90 234 Th ⟶ 91 234 Pa + -1 0 e ; 90 234 Th ⟶ 91 234 Pa + -1 0 e ; 91 234 Pa ⟶ 92 234 U + -1 0 e ; 91 234 Pa ⟶ 92 234 U + -1 0 e ; 92 234 U ⟶ 90 230 Th + 2 4 He 92 234 U ⟶ 90 230 Th + 2 4 He 90 230 Th ⟶ 88 226 Ra + 2 4 He 90 230 Th ⟶ 88 226 Ra + 2 4 He 88 226 Ra ⟶ 86 222 Rn + 2 4 He ; 88 226 Ra ⟶ 86 222 Rn + 2 4 He ; 86 222 Rn ⟶ 84 218 Po + 2 4 He 86 222 Rn ⟶ 84 218 Po + 2 4 He

Half-life is the time required for half the atoms in a sample to decay. Example (answers may vary): For C-14, the half-life is 5770 years. A 10-g sample of C-14 would contain 5 g of C-14 after 5770 years; a 0.20-g sample of C-14 would contain 0.10 g after 5770 years.

( 1 2 ) 0.04 = 0.973 ( 1 2 ) 0.04 = 0.973 or 97.3%

2 × × 10 3 y

(a) 3.8 billion years; (b) The rock would be younger than the age calculated in part (a). If Sr was originally in the rock, the amount produced by radioactive decay would equal the present amount minus the initial amount. As this amount would be smaller than the amount used to calculate the age of the rock and the age is proportional to the amount of Sr, the rock would be younger.

c = 0; This shows that no Pu-239 could remain since the formation of the earth. Consequently, the plutonium now present could not have been formed with the uranium.

(a) 83 212 Bi ⟶ 84 212 Po + -1 0 e ; 83 212 Bi ⟶ 84 212 Po + -1 0 e ; (b) 5 8 B ⟶ 4 8 B e + -1 0 e ; 5 8 B ⟶ 4 8 B e + -1 0 e ; (c) 92 238 U + 0 1 n ⟶ 93 239 Np + -1 0 N p , 92 238 U + 0 1 n ⟶ 93 239 Np + -1 0 N p , 93 239 Np ⟶ 94 239 Pu + -1 0 e ; 93 239 Np ⟶ 94 239 Pu + -1 0 e ; (d) 38 90 Sr ⟶ 39 90 Y + -1 0 e 38 90 Sr ⟶ 39 90 Y + -1 0 e

(a) 95 241 Am + 2 4 He ⟶ 97 244 Bk + 0 1 n ; 95 241 Am + 2 4 He ⟶ 97 244 Bk + 0 1 n ; (b) 94 239 Pu + 15 0 1 n ⟶ 100 254 Fm + 6 −1 0 e ; 94 239 Pu + 15 0 1 n ⟶ 100 254 Fm + 6 −1 0 e ; (c) 98 250 Cf + 5 11 B ⟶ 103 257 Lr + 4 0 1 n ; 98 250 Cf + 5 11 B ⟶ 103 257 Lr + 4 0 1 n ; (d) 98 249 Cf + 7 15 N ⟶ 105 260 Db + 4 0 1 n 98 249 Cf + 7 15 N ⟶ 105 260 Db + 4 0 1 n

Two nuclei must collide for fusion to occur. High temperatures are required to give the nuclei enough kinetic energy to overcome the very strong repulsion resulting from their positive charges.

A nuclear reactor consists of the following: 1. A nuclear fuel. A fissionable isotope must be present in large enough quantities to sustain a controlled chain reaction. The radioactive isotope is contained in tubes called fuel rods. 2. A moderator. A moderator slows neutrons produced by nuclear reactions so that they can be absorbed by the fuel and cause additional nuclear reactions. 3. A coolant. The coolant carries heat from the fission reaction to an external boiler and turbine where it is transformed into electricity. 4. A control system. The control system consists of control rods placed between fuel rods to absorb neutrons and is used to adjust the number of neutrons and keep the rate of the chain reaction at a safe level. 5. A shield and containment system. The function of this component is to protect workers from radiation produced by the nuclear reactions and to withstand the high pressures resulting from high-temperature reactions.

The fission of uranium generates heat, which is carried to an external steam generator (boiler). The resulting steam turns a turbine that powers an electrical generator.

Introduction of either radioactive Ag + or radioactive Cl – into the solution containing the stated reaction, with subsequent time given for equilibration, will produce a radioactive precipitate that was originally devoid of radiation.

(a) 53 133 I ⟶ 54 133 Xe + −1 0 e ; 53 133 I ⟶ 54 133 Xe + −1 0 e ; (b) 37.6 days

Alpha particles can be stopped by very thin shielding but have much stronger ionizing potential than beta particles, X-rays, and γ-rays. When inhaled, there is no protective skin covering the cells of the lungs, making it possible to damage the DNA in those cells and cause cancer.

(a) 7.64 × × 10 9 Bq; (b) 2.06 × × 10 −2 Ci

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Chemistry library

Welcome to the chemistry library, unit 1: atoms, compounds, and ions, unit 2: mass spectrometry, unit 3: chemical reactions and stoichiometry, unit 4: more about chemical reactions, unit 5: electronic structure of atoms, unit 6: periodic table, unit 7: chemical bonds, unit 8: gases and kinetic molecular theory, unit 9: states of matter and intermolecular forces, unit 10: chemical equilibrium, unit 11: acids and bases, unit 12: buffers, titrations, and solubility equilibria, unit 13: thermodynamics, unit 14: redox reactions and electrochemistry, unit 15: kinetics, unit 16: studying for the ap chemistry exam, unit 17: meet the chemistry professional.

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21.E: Nuclear Chemistry (Exercises)

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These are homework exercises to accompany the Textmap created for "Chemistry: The Central Science" by Brown et al. Complementary General Chemistry question banks can be found for other Textmaps and can be accessed here . In addition to these publicly available questions, access to private problems bank for use in exams and homework is available to faculty only on an individual basis; please contact Delmar Larsen for an account with access permission.

21.1: Radioactivity

Why are many radioactive substances warm to the touch? Why do many radioactive substances glow?

Describe the differences between nonionizing and ionizing radiation in terms of the intensity of energy emitted and the effect each has on an atom or molecule after collision. Which nuclear decay reactions are more likely to produce ionizing radiation? nonionizing radiation?

Would you expect nonionizing or ionizing radiation to be more effective at treating cancer? Why?

Ionizing radiation is higher in energy and causes greater tissue damage, so it is more likely to destroy cancerous cells.

Historically, concrete shelters have been used to protect people from nuclear blasts. Comment on the effectiveness of such shelters.

Gamma rays are a very high-energy radiation, yet α particles inflict more damage on biological tissue. Why?

List the three primary sources of naturally occurring radiation. Explain the factors that influence the dose that one receives throughout the year. Which is the largest contributor to overall exposure? Which is the most hazardous?

Three primary naturally occurring radiations are radium, uranium and thorium, each all having long half lives. Inhalation of air, ingestion of food and water,terrestrial radation from the ground and cosmic radiation from space are all factors tat influence the does that a person receives throughout the year. Inhalation of the air is the largest contributor to exposure. Radiation can damage DNA or kill cells. When radiation is exposed to your body, it will collide with atoms and this will change and damage your DNA.

Because radon is a noble gas, it is inert and generally unreactive. Despite this, exposure to even low concentrations of radon in air is quite dangerous. Describe the physical consequences of exposure to radon gas. Why are people who smoke more susceptible to these effects?

Most medical imaging uses isotopes that have extremely short half-lives. These isotopes usually undergo only one kind of nuclear decay reaction. Which kind of decay reaction is usually used? Why? Why would a short half-life be preferred in these cases?

Beta decay. Alfa decay can be easily stopped by paper, which means it can not be used to see inside people's body. Also, Gamma rays are really dangerous for human, that even a short period of time exploding to it will have negative effect on human body. Thus, Beta decay is the perfect choice. It can be used to see through human's body and stopped by aluminum or some other metals.

Since all these radioactive decays are harmful for human body, if the half time of these reactions are short, the time exploding to these reactions will be short too.

Which would you prefer: one exposure of 100 rem, or 10 exposures of 10 rem each? Explain your rationale.

Ten exposures of 10 rem are less likely to cause major damage.

A 2.14 kg sample of rock contains 0.0985 g of uranium. How much energy is emitted over 25 yr if 99.27% of the uranium is 238 U, which has a half-life of 4.46 × 10 9 yr, if each decay event is accompanied by the release of 4.039 MeV? If a 180 lb individual absorbs all of the emitted radiation, how much radiation has been absorbed in rads?

There is a story about a “radioactive boy scout” who attempted to convert thorium-232, which he isolated from about 1000 gas lantern mantles, to uranium-233 by bombarding the thorium with neutrons. The neutrons were generated via bombarding an aluminum target with α particles from the decay of americium-241, which was isolated from 100 smoke detectors. Write balanced nuclear reactions for these processes. The “radioactive boy scout” spent approximately 2 h/day with his experiment for 2 yr. Assuming that the alpha emission of americium has an energy of 5.24 MeV/particle and that the americium-241 was undergoing 3.5 × 10 6 decays/s, what was the exposure of the 60.0 kg scout in rads? The intrepid scientist apparently showed no ill effects from this exposure. Why? 241/95 Am---> 4/2 He + 237/93Np---> 4/2He + 233/91Pa----> 1/0n+ 232/91Th---> 1/1 H + 233/92 U By adding alpha particles to the products side of the reaction, he was able to reduce the mass number by 4 and the atomic number by 2 to get the products he wanted. Bombardment with neutrons and 1 H was required to lower to the mass number to get Th and then raise both the mass number and the atomic number to yield Uranium. 2 hours*365*2= 1460 hours of exposure.*60min/1hr*60s/1min= 5.26*10^6s of exposure 1MeV= (1.6022*10^-13 Joules) * (5.24 MeV/particle)*2 particles= 1.679*10^-12 Joules. (1.679*10^-12 Joules) * (1 amu/ 1.4924*10^-10 Joules)= 2.51*10^-13 amu E=mc^2 E=(2.51*10^-13 amu)(1.66*10^-22kg/amu)(2.9998*10^8m/s)^2= (3.75*10^-18 kgm^2/s)*(3.5*10^6 decays/s)= 1.31*10^-11 joules of exposure per second. The scientist showed no ill effects from this exposure because if we multiple the energy in joules of exposure per second, 1.31*10^-11, by the total amount of seconds of exposure, 5.26*10^6s, we find that he was only exposed to 6.9*10^-5 joules of radiation throughout the span of two years. This is a very small amount of radiation for such a long span of time. In order to plug in the values for this equation, we must convert the given MeV to Joules with the known conversion rate. Similarly, we must convert Joules to amu with another known conversion rate. Then we can plug in the values and multiply by c^2 but we must not forget to multiple the amu by the conversion rate to kg in order to yield Joules. After all of this is done, we multiple the amount of Joules of exposure per second by the total amount of exposure in seconds in order to find out the total amount of exposure over the two year span.

21.2: Patterns of Nuclear Stability

How do chemical reactions compare with nuclear reactions with respect to mass changes? Does either type of reaction violate the law of conservation of mass? Explain your answers.

Why is the amount of energy released by a nuclear reaction so much greater than the amount of energy released by a chemical reaction?

Explain why the mass of an atom is less than the sum of the masses of its component particles.

The stability of a nucleus can be described using two values. What are they, and how do they differ from each other?

In the days before true chemistry, ancient scholars (alchemists) attempted to find the philosopher’s stone, a material that would enable them to turn lead into gold. Is the conversion of Pb → Au energetically favorable? Explain why or why not.

Describe the energy barrier to nuclear fusion reactions and explain how it can be overcome.

Imagine that the universe is dying, the stars have burned out, and all the elements have undergone fusion or radioactive decay. What would be the most abundant element in this future universe? Why?

Numerous elements can undergo fission, but only a few can be used as fuels in a reactor. What aspect of nuclear fission allows a nuclear chain reaction to occur?

How are transmutation reactions and fusion reactions related? Describe the main impediment to fusion reactions and suggest one or two ways to surmount this difficulty.

Using the information provided in Chapter 33, complete each reaction and calculate the amount of energy released from each in kilojoules.

• 238 Pa → ? + β −
• 216 Fr → ? + α
• 199 Bi → ? + β +
• 194 Tl → ? + β +
• 171 Pt → ? + α
• 214 Pb → ? + β −

Using the information provided in Chapter 33, complete each reaction and calculate the amount of energy released from each in kilojoules per mole.

• \(_{91}^{234}\textrm{Pa}\rightarrow \,?+\,_{-1}^0\beta\)
• \(_{88}^{226}\textrm{Ra}\rightarrow \,?+\,_2^4\alpha\)

Using the information provided in Chapter 33, complete each reaction and then calculate the amount of energy released from each in kilojoules per mole.

• \(_{27}^{60}\textrm{Co}\rightarrow\,?+\,_{-1}^0\beta\) (The mass of cobalt-60 is 59.933817 amu.)
• technicium-94 (mass = 93.909657 amu) undergoing fission to produce chromium-52 and potassium-40

Using the information provided in Chapter 33, predict whether each reaction is favorable and the amount of energy released or required in megaelectronvolts and kilojoules per mole.

• the beta decay of bismuth-208 (mass = 207.979742 amu)
• the formation of lead-206 by alpha decay

Using the information provided, predict whether each reaction is favorable and the amount of energy released or required in megaelectronvolts and kilojoules per mole.

• alpha decay of oxygen-16
• alpha decay to produce chromium-52

Calculate the total nuclear binding energy (in megaelectronvolts) and the binding energy per nucleon for 87 Sr if the measured mass of 87 Sr is 86.908877 amu.

• the calculated mass
• the mass defect
• the nuclear binding energy
• the nuclear binding energy per nucleon

The experimentally determined mass of 29 S is 28.996610 amu. Find each of the following.

Calculate the amount of energy that is released by the neutron-induced fission of 235 U to give 141 Ba, 92 Kr (mass = 91.926156 amu), and three neutrons. Report your answer in electronvolts per atom and kilojoules per mole.

Calculate the amount of energy that is released by the neutron-induced fission of 235 U to give 90 Sr, 143 Xe, and three neutrons. Report your answer in electronvolts per atom and kilojoules per mole.

Calculate the amount of energy released or required by the fusion of helium-4 to produce the unstable beryllium-8 (mass = 8.00530510 amu). Report your answer in kilojoules per mole. Do you expect this to be a spontaneous reaction?

Calculate the amount of energy released by the fusion of 6 Li and deuterium to give two helium-4 nuclei. Express your answer in electronvolts per atom and kilojoules per mole.

How much energy is released by the fusion of two deuterium nuclei to give one tritium nucleus and one proton? How does this amount compare with the energy released by the fusion of a deuterium nucleus and a tritium nucleus, which is accompanied by ejection of a neutron? Express your answer in megaelectronvolts and kilojoules per mole. Pound for pound, which is a better choice for a fusion reactor fuel mixture?

Numerical Answers

• \(_{91}^{238}\textrm{Pa}\rightarrow\,_{92}^{238}\textrm{U}+\,_{-1}^0\beta\); −5.540 × 10 −16 kJ
• \(_{87}^{216}\textrm{Fr}\rightarrow\,_{85}^{212}\textrm{At}+\,_{2}^4\alpha\); −1.470 × 10 −15 kJ
• \(_{83}^{199}\textrm{Bi}\rightarrow\,_{82}^{199}\textrm{Pb}+\,_{+1}^0\beta\); −5.458 × 10 −16 kJ
• \(_{91}^{234}\textrm{Pa}\rightarrow\,_{92}^{234}\textrm{U}+\,_{-1}^0\beta\); 2.118 × 10 8 kJ/mol
• \(_{88}^{226}\textrm{Ra}\rightarrow\,_{86}^{222}\textrm{Rn}+\,_{2}^4\alpha\); 4.700 × 10 8 kJ/mol
• The beta decay of bismuth-208 to polonium is endothermic (ΔE = 1.400 MeV/atom, 1.352 × 10 8 kJ/mol).
• The formation of lead-206 by alpha decay of polonium-210 is exothermic (ΔE = −5.405 MeV/atom, −5.218 × 10 8 kJ/mol).
• 757 MeV/atom, 8.70 MeV/nucleon
• 53.438245 amu
• 0.496955 amu
• 463 MeV/atom
• 8.74 MeV/nucleon
• −173 MeV/atom; 1.67 × 10 10 kJ/mol
• ΔE = + 9.0 × 10 6 kJ/mol beryllium-8; no
• D–D fusion: ΔE = −4.03 MeV/tritium nucleus formed = −3.89 × 10 8 kJ/mol tritium; D–T fusion: ΔE = −17.6 MeV/tritium nucleus = −1.70 × 10 9 kJ/mol; D–T fusion

21.3: Nuclear Transmutations

Why do scientists believe that hydrogen is the building block of all other elements? Why do scientists believe that helium-4 is the building block of the heavier elements?

How does a star produce such enormous amounts of heat and light? How are elements heavier than Ni formed?

Propose an explanation for the observation that elements with even atomic numbers are more abundant than elements with odd atomic numbers.

The raw material for all elements with Z > 2 is helium (Z = 2), and fusion of helium nuclei will always produce nuclei with an even number of protons.

During the lifetime of a star, different reactions that form different elements are used to power the fusion furnace that keeps a star “lit.” Explain the different reactions that dominate in the different stages of a star’s life cycle and their effect on the temperature of the star.

A line in a popular song from the 1960s by Joni Mitchell stated, “We are stardust….” Does this statement have any merit or is it just poetic? Justify your answer.

If the laws of physics were different and the primary element in the universe were boron-11 (Z = 5), what would be the next four most abundant elements? Propose nuclear reactions for their formation.

Write a balanced nuclear reaction for the formation of each isotope.

• 27 Al from two 12 C nuclei
• 9 Be from two 4 He nuclei

At the end of a star’s life cycle, it can collapse, resulting in a supernova explosion that leads to the formation of heavy elements by multiple neutron-capture events. Write a balanced nuclear reaction for the formation of each isotope during such an explosion.

• 106 Pd from nickel-58
• selenium-79 from iron-56

When a star reaches middle age, helium-4 is converted to short-lived beryllium-8 (mass = 8.00530510 amu), which reacts with another helium-4 to produce carbon-12. How much energy is released in each reaction (in megaelectronvolts)? How many atoms of helium must be “burned” in this process to produce the same amount of energy obtained from the fusion of 1 mol of hydrogen atoms to give deuterium?

21.4: Rates of Radioactive Decay

What do chemists mean by the half-life of a reaction?

If a sample of one isotope undergoes more disintegrations per second than the same number of atoms of another isotope, how do their half-lives compare?

Half-lives for the reaction A + B → C were calculated at three values of [A] 0 , and [B] was the same in all cases. The data are listed in the following table:

Does this reaction follow first-order kinetics? On what do you base your answer?

• No; the reaction is second order in A because the half-life decreases with increasing reactant concentration according to t 1 /2 = 1/ k [A 0 ].

Ethyl-2-nitrobenzoate (NO 2 C 6 H 4 CO 2 C 2 H 5 ) hydrolyzes under basic conditions. A plot of [NO 2 C 6 H 4 CO 2 C 2 H 5 ] versus t was used to calculate t ½, with the following results:

Is this a first-order reaction? Explain your reasoning.

Azomethane (CH 3 N 2 CH 3 ) decomposes at 600 K to C 2 H 6 and N 2 . The decomposition is first order in azomethane. Calculate t ½ from the data in the following table:

How long will it take for the decomposition to be 99.9% complete?

t 1 /2 = 1.92 × 10 3 s or 1920 s; 19100 s or 5.32 hrs.

The first-order decomposition of hydrogen peroxide has a half-life of 10.7 h at 20°C. What is the rate constant (expressed in s −1 ) for this reaction? If you started with a solution that was 7.5 × 10 −3 M H 2 O 2 , what would be the initial rate of decomposition (M/s)? What would be the concentration of H 2 O 2 after 3.3 h?