Solution: Write an equation describing the radioactive decay

What if a nuclide undergoes two successive decays such that it becomes the original nuclide? Which decays could account for this? Provide an example.

Nuclear fission processes can provide a lot of energy but can also have safety concerns. What if Congress decided to outlaw all processes that involve fission? How would that change our society?

Define or illustrate the following terms. a. thermodynamic stability b. kinetic stability c. radioactive decay d. b-particle production e. a-particle production f. positron production g. electron capture h. g-ray emissions

Which type of radioactive decay has the net effect of changing a neutron into a proton? Which type of decay has the net effect of turning a proton into a neutron?

Supply the missing particle, and state the type of decay for each of the following nuclear processes. a. 238 92U 4 2He + ? b. 234 90 Th 234 91 Pa

Write an equation describing the radioactive decay of each of the following nuclides. (The particle produced is shown in parentheses, except for electron capture, where an electron is a reactant.) a. 3 1H (b) b. 8 3Li (b followed by a) c. 7 4Be (electron capture) d. 8 5B (positron)

Write balanced equations for each of the following processes. a. Chromium-51, which targets the spleen and is used as a tracer in studies of red blood cells, decays by electron capture. b. Iodine-131, used to treat hyperactive thyroid glands, decays by producing a b particle. c. Phosphorus-32, which accumulates in the liver, decays by b-particle production.

In each of the following radioactive decay processes, supply the missing particle. a. 73Ga n 73Ge 1 ? e. 60Co n 60Ni 1 ? b. 192Pt n 188Os 1 ? f. 97Tc 1 ? n 97Mo c. 205Bi n 205Pb 1 ? g. 99Tc n 99Ru 1 ? d. 241Cm 1 ? n 241Am h. 239Pu n 235U 1 ?

Write an equation describing the radioactive decay of each of the following nuclides. (The particle produced is shown in parentheses, except for electron capture, where an electron is a reactant.) a. 68Ga (electron capture) b. 62Cu (positron) c. 212Fr (a) d. 129Sb (b)

In the bismuth-214 natural decay series, Bi-214 initially undergoes b decay, the resulting daughter emits an a particle, and the succeeding daughters emit a b and a b particle in that order. Determine the product of each step in the Bi-214 decay series.

The radioactive isotope 247Bk decays by a series of a-particle and b-particle productions, taking 247Bk through many transformations to end up as 207Pb. In the complete decay series, how many a particles and b particles are produced?

Thorium-232 is known to undergo a progressive decay series until it reaches stability at lead-208. For each step of the series indicated in the table below, which nuclear particle is emitted? Parent Nuclide Particle Emitted Th-232 Ra-228 Ac-228 Th-228 Ra-224 Rn-220 Po-216 Pb-212 Bi-212 Po-212 Pb-208

One type of commercial smoke detector contains a minute amount of radioactive americium-241 (241Am), which decays by a-particle production. The a particles ionize molecules in the air, allowing it to conduct an electric current. When smoke particles enter, the conductivity of the air is changed and the alarm buzzes. a. Write the equation for the decay of 241 95Am by a-particle production. b. The complete decay of 241Am involves successively a, a, b, a, a, b, a, a, a, b, a, and b production. What is the final stable nucleus produced in this decay series? c. Identify the 11 intermediate nuclides

There are four stable isotopes of iron with mass numbers 54, 56, 57, and 58. There are also two radioactive isotopes: iron-53 and iron-59. Predict modes of decay for these two isotopes, and write a nuclear reaction for each. (See Table 20.2.)

The only stable isotope of fluorine is fluorine-19. Predict possible modes of decay for fluorine-21, fluorine-18, and fluorine-17

The only stable isotope of fluorine is fluorine-19. Predict possible modes of decay for fluorine-21, fluorine-18, and fluorine-17

In 1994 it was proposed (and eventually accepted) that element 106 be named seaborgium (Sg) in honor of Glenn T. Seaborg, discoverer of the transuranium elements. a. 263Sg was produced by the bombardment of 249Cf with a beam of 18O nuclei. Complete and balance an equation for this reaction. b. 263Sg decays by a-particle emission. What is the other product resulting from the a decay of 263Sg?

Many elements have been synthesized by bombarding relatively heavy atoms with high-energy particles in particle accelerators. Complete the following nuclear reactions, which have been used to synthesize elements. a. ______ 1 4 2He 88n 24 9 3 7Bk 1 1 0n b. 23 9 8 2U 1 12 6C 88n ______ 1 61 0n c. 24 9 9 8Cf 1 ______ 88n 2 1 6 0 0 5Db 1 41 0n d. 24 9 9 8Cf 1 10 5B 88n 2 1 5 0 7 3Lr 1 ______

Americium-241 is widely used in smoke detectors. The radiation released by this element ionizes particles that are then detected by a charged-particle collector. The halflife of 241Am is 433 years, and it decays by emitting alpha particles. How many alpha particles are emitted each second by a 5.00-g sample of 241Am?

Krypton consists of several radioactive isotopes, some of which are listed in the following table. Isotope Half-life Kr-73 27 s Kr-74 11.5 min Kr-76 14.8 h Kr-81 2.1 3 105 yr Which of these isotopes is most stable, and which isotope is hottest? How long does it take for 87.5% of each isotope to decay?

Radioactive copper-64 decays with a half-life of 12.8 days. a. What is the value of k in s21? b. A sample contains 28.0 mg 64Cu. How many decay events will be produced in the first second? Assume that the atomic mass of 64Cu is 64.0 u. c. A chemist obtains a fresh sample of 64Cu and measures its radioactivity. She then determines that to do an experiment, the radioactivity cannot fall below 25% of the initial measured value. How long does she have to perform the experiment?

The curie (Ci) is a commonly used unit for measuring nuclear radioactivity: 1 curie of radiation is equal to 3.7 3 1010 decay events per second (the number of decay events from 1 g of radium in 1 s). a. What mass of Na2 38SO4 has an activity of 10.0 mCi? Sulfur-38 has an atomic mass of 38.0 u and a halflife of 2.87 h. b. How long does it take for 99.99% of a sample of sulfur-38 to decay?

The first atomic explosion was detonated in the desert north of Alamogordo, New Mexico, on July 16, 1945. What percentage of the strontium-90 (t1/2 5 28.9 yr) originally produced by that explosion still remains as of July 16, 2016?

Iodine-131 is used in the diagnosis and treatment of thyroid disease and has a half-life of 8.0 days. If a patient with thyroid disease consumes a sample of Na131I containing 10. mg of 131I, how long will it take for the amount of 131I to decrease to 1/100 of the original amount?

Phosphorus-32 is a commonly used radioactive nuclide in biochemical research, particularly in studies of nucleic acids. The half-life of phosphorus-32 is 14.3 days. What mass of phosphorus-32 is left from an original sample of 175 mg of Na3 32PO4 after 35.0 days? Assume that the atomic mass of 32P is 32.0 u.

A chemist wishing to do an experiment requiring 47Ca21 (half-life 5 4.5 days) needs 5.0 mg of the nuclide. What mass of 47CaCO3 must be ordered if it takes 48 h for delivery from the supplier? Assume that the atomic mass of 47Ca is 47.0 u.

Explain the theory behind carbon-14 dating. What assumptions must be made and what problems arise when using carbon-14 dating?

The decay of uranium-238 to lead-206 is also used to estimate the age of objects. Specifically, 206Pb-to-238U ratios allow dating of rocks. Why is the 238U decay to 206Pb useful for dating rocks but useless for dating objects 10,000 years old or younger? Similarly, why is carbon-14 dating useful for dating objects 10,000 years old or younger but useless for dating rocks?

At a flea market youve found a very interesting painting done in the style of Rembrandts Dark Period (1642 1672). You suspect that you really do not have a genuine Rembrandt, so you take it to the local university for testing. Living wood shows a carbon-14 activity of 15.3 counts per minute per gram. Your painting showed a carbon-14 activity of 15.1 counts per minute per gram. Could it be a genuine Rembrandt? (For 14C, t1/2 5 5730 years.)

A living plant contains about the same fraction of carbon-14 as atmospheric carbon dioxide. The observed rate of decay of carbon-14 from a living plant is 15.3 counts per minute per gram of carbon. How many counts per minute per gram of carbon will be measured from a 15,000-year-old sample? Will radiocarbon dating work well for small samples of 10 mg or less? (For 14C, t1/2 5 5730 years.)

During World War II, tritium (3 H) was a component of fluorescent watch dials and hands. Assume you have such a watch that was made in January 1944. If 17% or more of the original tritium was needed to read the dial in dark places, until what year could you read the time at night? (For 3 H, t1/2 5 12.3 years.)

Define third-life in a similar way to half-life, and determine the third-life for a nuclide that has a half-life of 31.4 years.

Fresh rainwater or surface water contains enough tritium ( 3 1H) to show 5.5 decay events per minute per 100. g water. Tritium has a half-life of 12.3 years. You are asked to check a vintage wine that is claimed to have been produced in 1946. How many decay events per minute should you expect to observe in 100. g of that wine?

A proposed system for storing nuclear wastes involves storing the radioactive material in caves or deep mine shafts. One of the most toxic nuclides that must be disposed of is plutonium-239, which is produced in breeder reactors and has a half-life of 24,100 years. A suitable storage place must be geologically stable long enough for the activity of plutonium-239 to decrease to 0.1% of its original value. How long is this period for plutonium-239?

A rock contains 0.688 mg of 206Pb for every 1.000 mg of 238U present. Assuming that no lead was originally present, that all the 206Pb formed over the years has remained in the rock, and that the number of nuclides in intermediate stages of decay between 238U and 206Pb is negligible, calculate the age of the rock. (For 238U, t1/2 5 4.5 3 109 years.)

The mass ratios of 40Ar to 40K can also be used to date geological materials. Potassium-40 decays by two processes: 4 1 0 9K 1 21 0 e 88n 4 1 0 8Ar (10.7%) t1/2 5 1.27 3 109 yr 4 1 0 9K 88n 4 2 0 0Ca 1 21 0 e (89.3%) a. Why are 40Ar/40K ratios rather than 40Ca/40K ratios used to date materials? b. What assumptions must be made in using this technique? c. A sedimentary rock has a 40Ar/40K ratio of 0.95. Calculate the age of the rock. d. How will the measured age of a rock compare with the actual age if some 40Ar has escaped from the sample?

The sun radiates 3.9 3 1023 J of energy into space every second. What is the rate at which mass is lost from the sun?

The earth receives 1.8 3 1014 kJ/s of solar energy. What mass of solar material is converted to energy over a 24-h period to provide the daily amount of solar energy to the earth? What mass of coal would have to be burned to provide the same amount of energy? Coal releases 32 kJ of energy per gram when burned.

The most stable nucleus in terms of binding energy per nucleon is 56Fe. If the atomic mass of 56Fe is 55.9349 u, calculate the binding energy per nucleon for 56Fe

Calculate the binding energy per nucleon for 2 1H and 3 1H. The atomic masses are 2 1H, 2.01410 u, and 3 1H, 3.01605

Calculate the binding energy in J/nucleon for carbon-12 (atomic mass 5 12.00000 u) and uranium-235 (atomic mass 5 235.0439 u). The atomic mass of 1 1H is 1.00782 u, and the mass of a neutron is 1.00866 u. The most stable nucleus known is 56Fe (see Exercise 37). Would the binding energy per nucleon for 56Fe be larger or smaller than that for 12C or 235U? Explain

The mass defect for a lithium-6 nucleus is 20.03434 g/mol. Calculate the atomic mass of lithium-6.

The binding energy per nucleon for magnesium-27 is 1.326 3 10212 J/nucleon. Calculate the atomic mass of magnesium-27.

Consider the following reaction, which can take place in particle accelerators: 1 1H 1 1 0n h 2 1 1H 1 1 0n 1 1 21H Calculate the energy change for this reaction. Is energy released or absorbed? What is a possible source for this energy?

The easiest fusion reaction to initiate is 2 1H 1 3 1H 88n 4 2He 1 1 0n Calculate the energy released per nucleus of 4 2He produced and per mole of 4 2He produced. The atomic masses are as follows: 2 1H, 2.01410 u; 3 1H, 3.01605 u; and 4 2He, 4.00260 u. The masses of the electron and neutron are 5.4858 3 1024 u and 1.00866 u, respectively.

Calculate the amount of energy released per gram of hydrogen nuclei reacted for the following reaction. The atomic masses are 1 1H, 1.00782 u, and 2 1H, 2.01410 u. (Hint: Think carefully about how to account for the electron mass.) 1 1H 1 1 1H 88n 2 1H 1 11 0 e

The typical response of a Geiger-Mller tube is shown below. Explain the shape of this curve. Disintegrations/s from sample

When using a Geiger-Mller counter to measure radioactivity, one must maintain the same geometrical orientation between the sample and the Geiger-Mller tube to compare different measurements. Why?

Define fission and fusion. Fusion processes are more likely to occur for lighter elements, whereas fission processes are more likely to occur for heavier elements. Explain

Why are elevated temperatures necessary to initiate fusion reactions but not fission reactions?

What are the purposes of the moderator and control rods in a fission reactor

Breeder reactors are used to convert the nonfissionable nuclide 23 9 8 2U to a fissionable product. Neutron capture of the 23 9 8 2U is followed by two successive beta decays. What is the final fissionable product?

During the research that led to production of the two atomic bombs used against Japan in World War II, different mechanisms for obtaining a supercritical mass of fissionable material were investigated. In one type of bomb, a gun shot one piece of fissionable material into a cavity containing another piece of fissionable material. In the second type of bomb, the fissionable material was surrounded with a high explosive that, when detonated, compressed the fissionable material into a smaller volume. Discuss what is meant by critical mass, and explain why the ability to achieve a critical mass is essential to sustaining a nuclear reaction.

There is a trend in the United States toward using coalfired power plants to generate electricity rather than building new nuclear fission power plants. Is the use of coal-fired power plants without risk? Make a list of the risks to society from the use of each type of power plant.

How could a radioactive nuclide be used to demonstrate that chemical equilibrium is a dynamic process?

Consider the following reaction to produce methyl acetate: B CH3OH + CH3COH O B CH3COCH3 + H2O O Methyl acetate When this reaction is carried out with CH3OH containing radioactive oxygen-18, the water produced is not radioactive. Explain.

Photosynthesis in plants can be represented by the following overall reaction: 6CO2(g) 1 6H2O(l) 8888n C6H12O6(s) 1 6O2(g) Algae grown in water containing some radioactive 18O (in H2 18O) evolve oxygen gas with the same isotopic composition as the oxygen in the water. When algae growing in water containing only 16O were furnished with carbon dioxide containing 18O, no 18O was found to be evolved from the oxygen gas produced. What conclusions about photosynthesis can be drawn from these experiments?

Radiotracers are used in the medical sciences to learn about metabolic pathways. What are radiotracers? Explain why 14C and 32P radioactive nuclides would be very helpful in learning about metabolic pathways

The biological effects of a particular source of radiation depend on several factors. List some of these factors. Even though 85Kr and 90Sr are both b-particle emitters, the dangers associated with the decay of 90Sr are much greater than those linked to 85Kr. Why?

Although g rays are far more penetrating than a particles, the latter are more likely to cause damage to an organism. Why? Which type of radiation is more effective at promoting the ionization of biomolecules?

Consider the following information: i. The layer of dead skin on our bodies is sufficient to protect us from most a-particle radiation. ii. Plutonium is an a-particle producer. iii. The chemistry of Pu41 is similar to that of Fe31. iv. Pu oxidizes readily to Pu41. Why is plutonium one of the most toxic substances known?

Much of the research on controlled fusion focuses on the problem of how to contain the reacting material. Magnetic fields appear to be the most promising mode of containment. Why is containment such a problem? Why must one resort to magnetic fields for containment?

A positron and an electron can annihilate each other on colliding, producing energy as photons: 0 21e 1 0 11e h 2 0 0g Assuming that both g rays have the same energy, calculate the wavelength of the electromagnetic radiation produced.

Consider the following graph of binding energy per nucleon as a function of mass number. 9 8 7 6 5 4 3 2 1 0 Binding energy per nucleon (MeV) 20 40 60 80 100 120 140 160 180 200 220 240 260 2H 3He 3H 6Li 7Li 4He 14N 12C 16O 34S 56Fe 84Kr 119Sn 205Tl 235U 238U Mass number (A) a. What does this graph tell us about the relative halflives of the nuclides? Explain your answer. b. Which nuclide shown is the most thermodynamically stable? Which is the least thermodynamically stable? c. What does this graph tell us about which nuclides undergo fusion and which undergo fission to become more stable? Support your answer.

The mass percent of carbon in a typical human is 18%, and the mass percent of 14C in natural carbon is 1.6 3 10210%. Assuming a 180-lb person, how many decay events per second occur in this person due exclusively to the b-particle decay of 14C? (For 14C, t1/2 5 5730 years.)

Using the kinetic molecular theory (Section 5.6), calculate the root mean square velocity and the average kinetic energy of 1 2 H nuclei at a temperature of 4 3 107 K. (See Exercise 43 for the appropriate mass values.)

A small atomic bomb releases energy equivalent to the detonation of 20,000 tons of TNT; a ton of TNT releases 4 3 109 J of energy when exploded. Using 2 3 1013 J/mol as the energy released by fission of 235U, about what mass of 235U undergoes fission in this atomic bomb?

When nuclei undergo nuclear transformations, g rays of characteristic frequencies are observed. How does this fact, along with other information in the chapter on nuclear stability, suggest that a model similar to the quantum mechanics used for atoms may apply to the nucleus?

A chemist studied the reaction mechanism for the reaction 2NO(g) 1 O2(g) 88n 2NO2(g) by reacting N16O with 18O2. If the reaction mechanism is NO 1 O2 34 NO3 (fast equilibrium) NO3 1 NO 88n 2NO2 (slow) what distribution of 18O would you expect in the NO2? Assume that N is the central atom in NO3, assume only N16O18O2 forms, and assume stoichiometric amounts of reactants are combined.

Technetium-99 has been used as a radiographic agent in bone scans (9 4 9 3Tc is absorbed by bones). If 9 4 9 3Tc has a halflife of 6.0 hours, what fraction of an administered dose of 100. mg 9 4 9 3Tc remains in a patients body after 2.0 days?

A 0.10-cm3 sample of a solution containing a radioactive nuclide (5.0 3 103 counts per minute per milliliter) is injected into a rat. Several minutes later, 1.0 cm3 of blood is removed. The blood shows 48 counts of radioactivity per minute. What is the volume of blood in the rat? What assumptions must be made in performing this calculation?

In addition to the process described in the text, a second process called the carbonnitrogen cycle occurs in the sun: 1 1H 1 12 6C 88n 13 7N 1 0 0g 13 7N 88n 13 6C 1 11 0 e 1 1H 1 13 6C 88n 14 7N 1 0 0g 1 1H 1 14 7N 88n 15 8O 1 0 0g 15 8O 88n 15 7N 1 11 0 e 1 1H 1 15 7N 88n 12 6C 1 4 2He 1 0 0g Overall reaction: 4 1 1H 88n 4 2He 1 2 11 0 e a. What is the catalyst in the above scheme? b. What nucleons are intermediates? c. How much energy is released per mole of hydrogen nuclei reacted in the overall reaction? (See Exercises 43 and 44 for the appropriate mass values.)

Complete the following table with the nuclear particle that is produced in each nuclear reaction. Initial Nuclide Product Nuclide Particle Produced 23 9 9 4Pu 23 9 5 2U 21 8 4 2Pb 21 8 4 3Bi 6 2 0 7Co 6 2 0 8Ni 9 4 9 3Tc 9 4 9 4Ru 23 9 9 3Np 23 9 9 4Pu

A certain radioactive nuclide has a half-life of 3.00 hours. a. Calculate the rate constant in s21 for this nuclide. b. Calculate the decay rate in decays/s for 1.000 mole of this nuclide

Iodine-131 has a half-life of 8.0 days. How many days will it take for 174 g of 131I to decay to 83 g of 131I?

Rubidium-87 decays by b-particle production to strontium-87 with a half-life of 4.7 3 1010 years. What is the age of a rock sample that contains 109.7 mg of 87Rb and 3.1 mg of 87Sr? Assume that no 87Sr was present when the rock was formed. The atomic masses for 87Rb and 87Sr are 86.90919 u and 86.90888 u, respectively

Given the following information: Mass of proton 5 1.00728 u Mass of neutron 5 1.00866 u Mass of electron 5 5.486 3 1024 u Speed of light 5 2.9979 3 108 m/s Calculate the nuclear binding energy of 2 1 4 2Mg, which has an atomic mass of 23.9850 u.

Which of the following statement(s) is(are) true? a. A radioactive nuclide that decays from 1.00 3 1010 atoms to 2.5 3 109 atoms in 10 minutes has a half-life of 5.0 minutes. b. Nuclides with large Z values are observed to be a-particle producers. c. As Z increases, nuclides need a greater proton-toneutron ratio for stability. d. Those light nuclides that have twice as many neutrons as protons are expected to be stable.

Naturally occurring uranium is composed mostly of 238U and 235U, with relative abundances of 99.28% and 0.72%, respectively. The half-life for 238U is 4.5 3 109 years, and the half-life for 235U is 7.1 3 108 years. Assuming that the earth was formed 4.5 billion years ago, calculate the relative abundances of the 238U and 235U isotopes when the earth was formed

The curie (Ci) is a commonly used unit for measuring nuclear radioactivity: 1 curie of radiation is equal to 3.7 3 1010 decay events per second (the number of decay events from 1 g radium in 1 s). A 1.7-mL sample of water containing tritium was injected into a 150-lb person. The total activity of radiation injected was 86.5 mCi. After some time to allow the tritium activity to equally distribute throughout the body, a sample of blood plasma containing 2.0 mL water at an activity of 3.6 mCi was removed. From these data, calculate the mass percent of water in this 150-lb person.

Estimate the temperature needed to achieve the fusion of deuterium to make an a particle. The energy required can be estimated from Coulombs law [use the form E 5 9.0 3 109 (Q1Q2/r), using Q 5 1.6 3 10219 C for a proton and r 5 2 3 10215 m for the helium nucleus; the unit for the proportionality constant in Coloumbs law is J m/C2].

Radioactive cobalt-60 is used to study defects in vitamin B12 absorption because cobalt is the metallic atom at the center of the vitamin B12 molecule. The nuclear synthesis of this cobalt isotope involves a three-step process. The overall reaction is iron-58 reacting with two neutrons to produce cobalt-60 along with the emission of another particle. What particle is emitted in this nuclear synthesis? What is the binding energy in J per nucleon for the cobalt-60 nucleus (atomic masses 60Co 5 59.9338 u, 1 H 5 1.00782 u)? What is the de Broglie wavelength of the emitted particle if it has a velocity equal to 0.90c, where c is the speed of light?

To determine the Ksp value of Hg2I2, a chemist obtained a solid sample of Hg2I2 in which some of the iodine is present as radioactive 131I. The count rate of the Hg2I2 sample is 5.0 3 1011 counts per minute per mole of I. An excess amount of Hg2I2(s) is placed in some water, and the solid is allowed to come to equilibrium with its respective ions. A 150.0-mL sample of the saturated solution is withdrawn and the radioactivity measured at 33 counts per minute. From this information, calculate the Ksp value for Hg2I2. Hg2I2(s) 34 Hg2 21(aq) 1 2I2(aq) Ksp 5 [Hg2 21][I2]

The most significant source of natural radiation is radon-222. 222Rn, a decay product of 238U, is continuously generated in the earths crust allowing gaseous Rn to seep into the basements of buildings. Because 222Rn is an a-particle producer with a relatively short half-life of 3.82 days, it can cause biological damage when inhaled. a. How many a particles and b particles are produced when 238U decays to 222Rn? What nuclei is produced when 222Rn decays? b. Radon is a noble gas so one would expect it to pass through the body quickly. Why is there a concern over inhaling 222Rn? c. Another problem associated with 222Rn is that the decay of 222Rn produces a more potent a-particle producer (t1y2 5 3.11 min) that is a solid. What is the identity of the solid? Give the balanced equation of this species decaying by a-particle production. Why is the solid a more potent a-particle producer? d. The U.S. Environmental Protection Agency (EPA) recommends that 222Rn levels not exceed 4 pCi per liter of air (1 Ci 5 1 curie 5 3.7 3 1010 decay events per second; 1 pCi 5 1 3 10212 Ci). Convert 4.0 pCi per liter of air into concentration units of 222Rn atoms per liter of air and mole of 222Rn per liter of air

For uranium to be useful as a nuclear fuel, the relative amount of 235U to 238U must be increased from about 0.7% 235U in naturally occurring uranium to about 3%. The process of gas diffusion enrichment utilizes the velocity differences between 238UF6 and 235UF6 to accomplish the desired enrichment. Since the mass differences between 238UF6 and 235UF6 are relatively small, several steps are required in the diffusion process to enrich a natural uranium sample to the desired 3% 235U. (For a complete discussion of this process, see Section 5.7.) a. Which molecule, 238UF6 or 235UF6, has the greater average velocity at a certain temperature? Explain. b. In theory, how many steps are required to enrich a uranium sample from 0.700% 235U to 3.00% 235U using the UF6 multistage diffusion process? The molar masses of 235UF6 and 238UF6 are 349.03 g/mol and 352.05 g/mol, respectively. c. A certain sample of uranium is reacted with fluorine to form a mixture of 235UF6(g) and 238UF6(g). After 100 diffusion steps, the gas contains 1526 235UF6 molecules per 1.000 3 105 total number of molecules in the gas (235UF6 1 238UF6). What is the ratio of 235U to 238U atoms in the original sample of uranium?

Zirconium is one of the few metals that retains its structural integrity upon exposure to radiation. The fuel rods in most nuclear reactors therefore are often made of zirconium. Answer the following questions about the redox properties of zirconium based on the half-reaction ZrO2 ? H2O 1 H2O 1 4e2 88n Zr 1 4OH2 %8 5 22.36 V a. Is zirconium metal capable of reducing water to form hydrogen gas at standard conditions? b. Write a balanced equation for the reduction of water by zirconium. c. Calculate %8, DG8, and K for the reduction of water by zirconium metal. d. The reduction of water by zirconium occurred during the accident at Three Mile Island in 1979. The hydrogen produced was successfully vented and no chemical explosion occurred. If 1.00 3 103 kg of Zr reacts, what mass of H2 is produced? What volume of H2 at 1.0 atm and 1000.8C is produced? e. At Chernobyl in 1986, hydrogen was produced by the reaction of superheated steam with the graphite reactor core: C(s) 1 H2O(g) 88n CO(g) 1 H2(g) It was not possible to prevent a chemical explosion at Chernobyl. In light of this, do you think it was a correct decision to vent the hydrogen and other radioactive gases into the atmosphere at Three Mile Island? Explain.