Solved: Complete and balance the following nuclear equations by supplying the missing

Indicate whether each of the following nuclides lies within the belt of stability in Figure 21.3: (a) neon-24, (b) chlorine-32, (c) tin-108, (d) polonium-216. For any that do not, describe a nuclear decay process that would alter the neutron-to-proton ratio in the direction of increased stability. [Section 21.2]

Write the balanced nuclear equation for the reaction represented by the diagram shown here. [Section 21.2]

Draw a diagram similar to that shown in Exercise 21.2 that illustrates the nuclear reaction 2 Bi ---> He + 2 gjTl. [Section 21.2]

The accompanying graph illustrates the decay of Mo, which decays via positron emission. (a) What is the halflife of the decay? (b) What is the rate constant for the decay? (c) What fraction of the original sample of Mo remains after 12 minutes? (d) What is the product of the decay process? [Section 21.4]

A 1!r,/Ru atom has a mass of 99.90422 amu. (a) Why is the mass of this nuclide not much closer to 100? (b) Explain the observed mass using Figure 21.13. (c) Calculate the binding energy per nucleon for 1!r,/Ru. [Section 21.6]

The diagram shown below illustrates a fission process. (a) What is the second nuclear product of the fission? (b) Use Figure 21.3 to predict whether the nuclear products of this fission reaction are stable. [Section 21.7]

Indicate the number of protons and neutrons in the following nuclei: (a) n, (b) 2 01Hg, (c) potassium-39

Indicate the number of protons and neutrons in the following nuclei: (a) 1ggcs, (b) 119Sn, (c) barium-141.

Give the symbol for (a) a neutron, (b) an alpha particle, (c) gamma radiation

Write balanced nuclear equations for the following processes: (a) rubidium-90 undergoes beta decay; (b) selenium-72 undergoes electron capture; (c) krypton-76 undergoes positron emission; (d) radium-226 emits alpha radiation.

Write balanced nuclear equations for the following transformations: (a) gold-191 undergoes electron capture; (b) gold-201 decays to a mercury isotope; (c) gold198 undergoes beta decay; (d) gold-188 decays by positron emission.

Decay of which nucleus will lead to the following products: (a) bismuth-211 by beta decay; (b) chromium-50 by positron emission; (c) tantalum-179 by electron capture; (d) radium-226 by alpha decay?

What particle is produced during the following decay processes: (a) sodium-24 decays to magnesium-24; (b) mercury-188 decays to gold-188; (c) iodine-122 decays to xenon-122; (d) plutonium-242 decays to uranium-238?

The naturally occurring radioactive decay series that begins with U stops with formation of the stable z gPb nucleus. The decays proceed through a series of alpha-particle and beta-particle emissions. How many of each type of emission are involved in this series?

A radioactive decay series that begins with 2 ijTh ends with formation of the stable nuclide 2 Pb. How many alpha-particle emissions and how many beta-particle emissions are involved in the sequence of radioactive decays?

Predict the type of radioactive decay process for the following radionuclides: (a) B, (b) Cu, (c) phosphorus32, (d) chlorine-39.

Each of the following nuclei undergoes either beta or positron emission. Predict the type of emission for each: (a) Ge, (b) 'SRh, (c) iodine-137, (d) cerium-133.

One of the nuclides in each of the following pairs is radioactive. Predict which is radioactive and which is stable: (a) K and K, (b) 209Bi and 208Bi, (c) nickel-58 and nickel-65. Explain.

Which of the following nuclides have magic numbers of both protons and neutrons: (a) helium-4, (b) oxygen-18, (c) calcium-40, (d) zinc-66, (e) lead-208?

Tin has 10 stable isotopes, but antimony only has two. How can we explain this difference?

Using the concept of magic numbers, explain why alpha emission is relatively common, but proton emission is nonexistent.

Which of the following nuclides would you expect to be radioactive: Ni, Scu, 'SAg, tungsten-184, polonium206? Justify your choices.

Why are nuclear transmutations involving neutrons generally easier to accomplish than those involving protons or alpha particles?

Rutherford was able to carry out the first nuclear transmutation reactions by bombarding nitrogen-14 nuclei with alpha particles. 1n the famous experiment on scattering of alpha particles by gold foil (Section 2.2), however, a nuclear transmutation reaction did not occur. What is the difference between the two experiments? What would one need to do to carry out a successful nuclear transmutation reaction involving gold nuclei and alpha particles?

Complete and balance the following nuclear equations by supplying the missing particle: (a) 2f + 'gs ----> 3 bn + ? (b) yH + iHe ----> He + ? (c) !H + 1 3B ----> 3? (d) 1 1 ----> 1e + ? (e) iFe ----> - e + ?

Complete and balance the following nuclear equations by supplying the missing particle: IP + ? (b) Be + - e (orbital electron) --> ? (c) ? ----> Os + _ e (d) Mo + yH ----> /in + ? (e) 2 iu + 6n ----> 1We + 2 6n + ?

Write balanced equations for (a) U(a, n)23lPu, (b) 1N(a, p)10, (c) Fe( a, {3)Cu.

Each statement below refers to a comparison between two radioisotopes, A and X. Indicate whether each of the following statements is true or false, and why. (a) If the half-life for A is shorter than the half-life for X, A has a larger decay rate constant. (b) If X is "not radioactive," its half-life is essentially zero. (c) If A has a half-life of 10 years, and X has a half-life of 10,000 years, A would be a more suitable radioisotope to measure processes occurring on the 40-year time scale

It has been suggested that strontium-90 (generated by nuclear testing) deposited in the hot desert will undergo radioactive decay more rapidly because it will be exposed to much higher average temperatures. (a) Is this a reasonable suggestion? (b) Does the process of radioactive decay have an activation energy, like the Arrhenius behavior of many chemical reactions oco (Section 14.5)? Discuss.

The half-life of tritium (hydrogen-3) is 12.3 yr. If 56.2 mg of tritium is released from a nuclear power plant during the course of an accident, what mass of this nuclide will remain after 12.3 yr? After 100 yr?

It takes 5.2 minutes for a 1.000-g sample of210pr to decay to 0.250 g. What is the half-life of 210Fr?

Cobalt-60 is a strong gamma emitter that has a half-life of 5.26 yr. The cobalt-60 in a radiotherapy unit must be replaced when its radioactivity falls to 75% of the original sample. (a) If an original sample was purchased in June 2006, when will it be necessary to replace the cobalt-60? (b) How can you store cobalt-60 so that it is safe to handle?

How much time is required for a 6.25-mg sample of 51Cr to decay to 0.75 mg if it has a half-life of 27.8 days

Radium-226, which undergoes alpha decay, has a halflife of 1600 yr. (a) How many alpharticles are emitted in 5.0 min by a 10.0-mg sample of 6Ra? (b) What is the activity of the sample in mCi?

Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr. (a) How many beta particles are emitted in 180 s by a 3.75-mg sample of 60Co? (b) What is the activity of the sample in Bq?

The cloth shroud from around a mummy is found to have a 1 4C activity of 9.7 disintegrations per minute per gram of carbon as compared with living organisms that undergo 16.3 disintegrations per minute per gram of carbon. From the half-life for 14C decay, 5715 yr, calculate the age of the shroud.

Potassium-40 decays to argon-40 with a half-life of 1.27 X 109 yr. What is the age of a rock in which the mass ratio of 40 Ar to 40K is 4.2?

The half-life for the process 238u ----> 206Pb is 4.5 x 109 yr. A mineral sample contains 75.0 mg of 238U and 18.0 mg of 206Pb. What is the age of the mineral?

The !hermite reaction, Fe203(s) + 2 Al(s) ----> 2 Fe(s) + Al203(s), is one of the most exothermic reactions known. The heat released is sufficient to melt the iron product; consequently, the !hermite reaction is used to weld metal under the ocean. t.H0 for the !hermite reaction is -851.5 kJ/mole. What is the mass change per mole of Fe203 that accompanies this reaction?

An analytical laboratory balance typically measures mass to the nearest 0.1 mg. What energy change would accompany the loss of 0.1 mg in mass?

How much energy must be supplied to break a single aluminum-27 nucleus into separated protons and neutrons if an aluminum-27 atom has a mass of 26.9815386 amu? How much energy is required for 100.0 grams of aluminum-27? (The mass of an electron is given on the inside back cover.)

How much energy must be supplied to break a single 21Ne nucleus into separated protons and neutrons if the nucleus has a mass of 20.98846 amu? What is the nuclear binding energy for 1 mol of 21Ne?

Calculate the binding energy per nucleon for the following nuclei: (a) 1C (nuclear mass, 11.996708 amu); (b) 3 7Cl (nuclear mass, 36.956576 amu); (c) rhodium-103 (atomic mass, 102.905504 amu).

Calculate the binding energy per nucleon for the following nuclei: (a) 1N (nuclear mass, 13.999234 amu); (b) 4i (nuclear mass, 47.935878 amu); (c) xenon-129 (atomic mass, 128.904779 amu)

The energy from solar radiation falling on Earth is 1.07 X 1016 kJ/min. (a) How much loss of mass from the Sun occurs in one day from just the energy falling on Earth? (b) If the energy released in the reaction 235U + bn ----> 1t6Ba + Kr + 3 bn ( 235U nuclear mass, 234.9935 amu; 141Ba nuclear mass, 140.8833 amu; 9 2Kr nuclear mass, 91.9021 amu) is taken as typical of that occurring in a nuclear reactor, what mass of uranium-235 is required to equal 0.10% of the solar energy that falls on Earth in 1.0 day?

Which of the following nuclei is likely to have the lar est mass defect per nucleon: (a) 59Co, (b) 11B, (c) 18Sn, (d) 2 4 3Cm? Explain your answer.

Based on Figure 21.13, what is the most stable nucleus in the periodic table?

Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a halflife of 8.02 days. The thyroid is the only gland in the body that uses iodine. A person undergoing a test of thyroid activity drinks a solution of Nal, in which only a small fraction of the iodide is radioactive. (a) Why is Nal a good choice for the source of iodine? (b) If a Geiger counter is placed near the person's thyroid (which is near the neck) right after the sodium iodide solution is taken, what will the data look like as a function of time? (c) A normal thyroid will take up about 12% of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to 0.01% of the original amount?

Chlorine-36 is a convenient radiotracer. It is a weak beta emitter, with 1 1 /2 = 3 X 10 5 yr. Describe how you would use this radiotracer to carry out each of the following experiments. (a) Determine whether trichloroacetic acid, CC13COOH, undergoes any ionization of its chlorines as chloride ion in aqueous solution. (b) Demonstrate that the equilibrium between dissolved BaC12 and solid BaC12 in a saturated solution is a dynamic process. (c) Determine the effects of soil pH on the uptake of chloride ion from the soil by soybeans.

Explain the following terms that apply to fission reactions: (a) chain reaction, (b) critical mass.

Explain the function of the following components of a nuclear reactor: (a) control rods, (b) moderator.

Complete and balance the nuclear equations for the following fission or fusion reactions: (a) tH + tH ----. He + _ (b) 2U + bn ----. Sb + Nb + _ bn

Complete and balance the nuclear equations for the following fission reactions: (a) U + 6n ----. 1gSm + Zn + _ 6n (b) 2Pu + 6n ----. 1Ce + _ + 2 bn

A portion of the Sun's energy comes from the reaction 4 jH ----. 1He + 2 e This reaction requires a temperature of about 1o6 to 107K. (a) Why is such a high temperature required? (b) Is the Sun solid?

Hydroxyl radicals can pluck hydrogen atoms from molecules ("hydrogen abstraction"), and hydroxide ions can pluck protons from molecules ("deprotonation"). Write the reaction equations and Lewis dot structures for the hydrogen abstraction and deprotonation reactions for the generic carboxylic acid R-COOH with hydroxyl radical and hydroxide ion, respectively. Why is hydroxyl radical more toxic to living systems than hydroxide ion?

Use Lewis structures to represent the reactants and products in Equation 21.31. Why is the H2 0+ ion a free radical species?

A laboratory rat is exposed to an alpha-radiation source whose activity is 14.3 mCi. (a) What is the activity of the radiation in disintegrations per second? In becquerels? (b) The rat has a mass of 385 g and is exposed to the radiation for 14.0 s, absorbing 35% of the emitted alpha particles, each having an energy of 9.12 x 10-13 }. Calculate the absorbed dose in millirads and grays. (c) If the RBE of the radiation is 9.5, calculate the effective absorbed dose in mrem and Sv.

A 65-kg person is accidentally exposed for 240 s to a 15-mCi source of beta radiation coming from a sample of 90Sr. (a) What is the activity of the radiation source in disintegrations per second? In becquerels? (b) Each beta particle has an energy of 8.75 x 10-14 }, and 7.5% of the radiation is absorbed by the person. Assuming that the absorbed radiation is spread over the person's entire body, calculate the absorbed dose in rads and in grays. (c) If the RBE of the beta particles is 1.0, what is the effective dose in mrem and in sieverts? (d) How does the magnitude of this dose of radiation compare with that of a mammogram (300 mrem)?

Radon-222 decays to a stable nucleus by a series of three alpha emissions and two beta emissions. What is the stable nucleus that is formed?

A free neutron is unstable and decays into a proton with a half-life of 10.4 min. (a) What other particle forms? (b) Why don't neutrons in atomic nuclei decay at the same rate?

Americium-241 is an alpha emitter used in smoke detectors. The alpha radiation ionizes molecules in an air-filled gap between two electrodes in the smoke detector, leading to current. When smoke is present, the ionized molecules bind to smoke particles and the current decreases; when the current is reduced sufficiently, an alarm sounds. (a) Write the nuclear equation corresponding to the alpha decay of americiurn-241. (b) Why is an alpha emitter a better choice than a gamma emitter for a smoke detector? (c) In a commercial smoke detector, only 0.2 micrograms of americium are present. Calculate the energy that is equivalent to the mass loss of this amount of americium due to alpha radiation. The atomic mass of americium-241 is 241.056829 amu. (d) The half-life of americium-241 is 432 years; the half life of americium-240 is 2.12 days. Why is the 241 isotope a better choice for a smoke detector?

Chlorine has two stable nuclides, 3 5CJ and 3 7CJ. In contrast, 36CJ is a radioactive nuclide that decays by beta emission. (a) What is the product of decay of 36Cl? (b) Based on the empirical rules about nuclear stability, explain why the nucleus of 3 6Cl is less stable than either 3 5Cl or 3 7Cl.

Nuclear scientists have synthesized approximately 1600 nuclei not known in nature. More might be discovered with heavy-ion bombardment using high-energy particle accelerators. Complete and balance the following reactions, which involve heavy-ion bombardments: (a) Li + Ni ----. ? (b) 18Ca + 2Cm ----. Sm +? (c) Sr + Kr ----. 1Pd + ? (d) 18ca + 2u ----. 8zn + 4 6n + 2?

According to current regulations, the maximum permissible dose of strontium-90 in the body of an adult is 1

Suppose you had a detection device that could count every decay event from a radioactive sample of plutonium239 (11 12 is 24,000 yr). How many counts per second would you obtain from a sample containing 0.385 g of plutonium-239?

Methyl acetate (CH3COOCH3) is formed by the reaction of acetic acid with methyl alcohol. If the methyl alcohol is labeled with oxygen-18, the oxygen-18 ends up in the methyl acetate: 0 0 II II CH3COH + H180CH3 -------> CH3C180CH3 + H20 Do the C-OH bond of the acid and the 0-H bond of the alcohol break in the reaction, or do the 0-H bond of the acid and the C -OH bond of the alcohol break? Explain.

An experiment was designed to determine whether an aquatic plant absorbed iodide ion from water. Iodine131 (tl/2 = 8.02 days) was added as a tracer, in the form of iodide ion, to a tank containing the plants. The initial activity of a 1.00-

The nuclear masses of 7Be, 9Be, and 10Be are 7.0147, 9.0100, and 10.0113 amu, respectively. Which of these nuclei has the largest binding energy per nucleon?

A 26.00-g sample of water containing tritium, fH, emits 1.50 x 103 beta particles per second. Tritium is a weak beta emitter, with a half-life of 12.3 yr. What fraction of all the hydrogen in the water sample is tritium?

The Sun radiates energy into space at the rate of 3.9 x 1026 J/s. (a) Calculate the rate of mass loss from the Sun in kgjs. (b) How does this mass loss arise? (c) It is estimated that the Sun contains 9 X 1056 free protons. How many protons per second are consumed in nuclear reactions in the Sun?

The average energy released in the fission of a single uranium-235 nucleus is about 3 X 10-11 J. If the conversion of this energy to electricity in a nuclear power plant is 40% efficient, what mass of uranium-235 undergoes fission in a year in a plant that produces 1000 MW (megawatts)? Recall that a watt is 1 J/s.

Tests on human subjects in Boston in 1965 and 1966, following the era of atomic bomb testing, revealed average quantities of about 2 pCi of plutonium radioactivity in the average person. How many disintegrations per second does this level of activity imply? If each alpha particle deposits 8 X 10-1 3 J of energy and if the average person weighs 75 kg, calculate the number of rads and rems of radiation in 1 yr from such a level of plutonium.

Calculate the mass of octane, C8H18 (/), that must be burned in air to evolve the same quantity of energy as produced by the fusion of 1.0 g of hydrogen in the following fusion reaction: 4 jH ----> He + 2 qe Assume that all the products of the combustion of octane are in their gas phases. Use data from Exercise 21.50, Appendix C, and the inside covers of the text. The standard enthalpy of formation of octane is -250.1 kJ/mol.

A sample of an alpha emitter having an activity of 0.18 Ci is stored in a 25.0-mL sealed container at 22 oc for 245 days. (a) How many alpha particles are formed during this time? (b) Assuming that each alpha particle is converted to a helium atom, what is the partial pressure of helium gas in the container after this 245-day period?

Charcoal samples from Stonehenge in England were burned in 02, and the resultant C02 gas bubbled into a solution of Ca(OHh (limewater), resulting in the precipitation of CaC03. The CaC03 was removed by filtration and dried. A 788-mg sample of the CaC03 had a radioactivity of 1.5 X 10-2 Bq due to carbon-14. By comparison, living organisms undergo 15.3 disintegrations per minute per gram of carbon. Using the half-life of carbon-14, 5715 yr, calculate the age of the charcoal sample.

When a positron is annihilated by combination with an electron, two photons of equal energy result. What is the wavelength of these photons? Are they gamma ray photons?

A 25.0-mLsample of 0.050 M barium nitrate solution was mixed with 25.0 mL of 0.050 M sodium sulfate solution labeled with radioactive sulfur-35. The activity of the initial sodium sulfate solution was 1.22 X 106 Bq/mL. After the resultant precipitate was removed by filtration, the remaining filtrate was found to have an activity of 250 Bq/mL. (a) Write a balanced chemical equation for the reaction that occurred. (b) Calculate the Ksp for the precipitate under the conditions of the experiment.