21. Nuclear Chemistry

The mass number of an isotope is

An alpha particle consists of __________ .

What is the daughter nuclide produced when Po-218 undergoes alpha decay?

In beta decay, the effective change in the nucleus is

What is the parent nuclide of the nuclear reaction that produces the daughter nuclide Hg-208 when undergoing beta decay?

Gamma rays are

The daughter nuclide of positron emission will differ from the parent nuclide by

What type of radioactive decay would result from an isotope with 40 protons and 80 neutrons?

Which of the following units takes into consideration the amount of damage to biological molecules?

A N/Z ratio close to 1 is most stable

Determine the age of a bone that has a decay rate of 3.80 dis/min ⋅ g C if the ratio of ¹²C:¹⁴C in living organisms has a decay rate of 15.3 dis/min ⋅ g C. (t_1/2 of ¹⁴C = 5730 years).

What is the balanced nuclear equation for the alpha decay of plutonium-238? (a) (b) (c) (d)

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

Fluorine-18 undergoes positron emission with a half-life of 1.10 x 10^2 minutes. If a patient is given a 250 mg dose for a PET scan, how long will it take for the amount of fluorine-18 to drop to 75 mg? (a) 56 minutes (b) 96 minutes (c) 132 minutes (d) 191 minutes

The steps below show three of the steps in the radioactive decay chain for 23290Th. The half-life of each isotope is shown below the symbol of the isotope. (d) The next step in the decay chain is an alpha emission. What is the next isotope in the chain? [Sections 21.2 and 21.4]

The steps below show three of the steps in the radioactive decay chain for 23290Th. The half-life of each isotope is shown below the symbol of the isotope. (a) Identify the type of radioactive decay for each of the steps (i), (ii), and (iii). [Sections 21.2 and 21.4]

The accompanying graph illustrates the decay of 8842Mo, which decays via positron emission. (d) What is the product of the decay process? [Section 21.4]

The accompanying graph illustrates the decay of 8842Mo, which decays via positron emission. (c) What fraction of the original sample of 8842Mo remains after 12 min? [Section 21.4]

In a cave in Oregon, archaeologists found bones, plant remains, and fossilized feces. DNA remaining in the feces indi-cates their human origin but not their age. To date the remains, the decay rate was measured and found to be 2.71 disinte-grations/min per gram of carbon. Currently living organisms have a decay rate of 15.3 disintegrations/min per gram of carbon, and the half-life of 14C is 5715 years. How old are the remains? (a) 1460 years (b) 9900 years (c) 14300 years (d) 18600 years

The accompanying graph illustrates the decay of 8842Mo, which decays via positron emission. (b) What is the rate constant for the decay? [Section 21.4]

The accompanying graph illustrates the decay of 8842Mo, which decays via positron emission. (a) What is the halflife of the decay? [Section 21.4]

Identify the true statement about nuclear power plants and nuclear weapons. (a) Nuclear power plants and nuclear weapons both use uranium enriched to about 90% U-235. (b) Nuclear power plants emit large amounts of CO2 just like coal burning power plants. (c) The United States produces less than 1% of its electrical power from nuclear energy. (d) A nuclear weapon explodes when two pieces of fission-able uranium-235 are pushed together to reach a critical mass.

How much energy in kJ/mol is released by the fission of uranium-235 to form barium-140 and krypton-93? The atomic masses are (a) 6.59 x 10^9 kJ/mol (b) 1.66 x 10^10 kJ/mol (c) 1.98 x 10^11 kJ/mol (d) 1.66 x 10^16 kJ/mol

Give the symbol for (c) gamma radiation.

Give the symbol for (b) an alpha particle.

Give the symbol for (c) a positron.

Give the symbol for (b) a beta particle.

Write balanced nuclear equations for the following processes: (c) krypton-76 undergoes positron emission.

Write balanced nuclear equations for the following transformations: (c) technicium-98 undergoes electron capture.

Write balanced nuclear equations for the following transformations: (a) bismuth-213 undergoes alpha decay.

Decay of which nucleus will lead to the following products: (a) bismuth-211 by beta decay?

Decay of which nucleus will lead to the following products: (b) chromium-50 by positron emission?

Decay of which nucleus will lead to the following products: (c) tantalum-179 by electron capture?

What particle is produced during the following decay processes: (c) iodine-122 decays to xenon-122?

Isotope A decays to isotope E through the following series of steps, in which the products of the individual decay events are themselves radioactive and undergo further decay until a stable nucleus is ultimately reached. Two kinds of processes are represented, one by the shorter arrows pointing right and the other by the longer arrows pointing left. (b) Identify and write the symbol for each isotope in the series:

Positron emission and electron capture both give a product nucleus whose atomic number is 1 less than the starting nucleus. Explain.

What is the difference between an a particle and a helium atom?

Why does beta emission raise the atomic number of the product while positron emission lowers. the atomic number?

Why does gamma emission not change the atomic number of the product?

Complete and balance the following nuclear equations by supplying the missing particle: (e) 5926Fe¡ 0-1e + ?

Complete and balance the following nuclear equations. (a)

Complete and balance the following nuclear equations. (b)

Complete and balance the following nuclear equations. (d)

Complete and balance the following nuclear equations. (a)

Complete and balance the following nuclear equations. (b)

Write a nuclear equation for the indicated decay of each nuclide. d. N-13 (positron emission)

Write a nuclear equation for the indicated decay of each nuclide. e. Cr-51 (electron capture)

Write a nuclear equation for the indicated decay of each nuclide. c. Pb-214 (beta)

Write a nuclear equation for the indicated decay of each nuclide. a. U-234 (alpha)

What particle is produced by the decay of thorium-214 to radium-210?

Write a nuclear equation for the indicated decay of each nuclide. e. Pd-103 (electron capture)

What particle is produced by the decay of uranium-239 to neptunium-239?

Write a partial decay series for Th-232 undergoing the sequential decays: a, b, b, a.

Each statement that follows refers to a comparison between two radioisotopes, A and X. Indicate whether each of the following statements is true or false. (a) If the half-life for A is shorter than the half-life for X, A has a larger decay rate constant.

What particle is produced in each of the following decay reactions? (c)

What particle is produced in each of the following decay reactions? (b)

What particle is produced in each of the following decay reactions? (a)

Write a partial decay series for Rn-220 undergoing the sequential decays: a, a, b, b.

What particle is produced in each of the following decay reactions? (c)

What particle is produced in each of the following decay reactions? (b)

What particle is produced in each of the following decay reactions? (a)

Fill in the missing particles in each nuclear equation. c. 1911Ne ¡1910Ne + ____

Some watch dials are coated with a phosphor, like ZnS, and a polymer in which some of the 1H atoms have been replaced by 3H atoms, tritium. The phosphor emits light when struck by the beta particle from the tritium decay, causing the dials to glow in the dark. The half-life of tritium is 12.3 yr. If the light given off is assumed to be directly proportional to the amount of tritium, by how much will a dial be dimmed in a watch that is 50 yr old?

Write balanced nuclear equations for the following processes. (b) Electron capture of 138Sm

Write balanced nuclear equations for the following processes. (c) Beta emission of 188W

Write balanced nuclear equations for the following processes. (a) Alpha emission of 162Re

Fill in the missing particles in each nuclear equation. d. 7535Br ¡ ____ + 0+1e

Fill in the missing particles in each nuclear equation. a. 24195Am ¡23793Np + ____

Fill in the missing particles in each nuclear equation. b. _____ ¡23392U + 0-1e

Fill in the missing particles in each nuclear equation. c. 23793 Np ¡ _____ +42He

It takes 4 h 39 min for a 2.00-mg sample of radium-230 to decay to 0.25 mg. What is the half-life of radium-230?

Write balanced nuclear equations for the following processes. (b) Electron capture of 126Ba

Write balanced nuclear equations for the following processes. (a) Beta emission of 157Eu

Write balanced nuclear equations for the following processes. (c) Alpha emission of 146Sm

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. If an original sample was purchased in June 2016, when will it be necessary to replace the cobalt-60?

226Ac can decay by any of three different nuclear processes: a emission, b emission, or electron capture. Write a balanced nuclear equation for the decay of 226Ac by each process.

The cloth shroud from around a mummy is found to have a 14C 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 * 109 yr. What is the age of a rock in which the mass ratio of 40Ar to 40K is 4.2?

Americium-241, a radioisotope used in smoke detectors, decays by a series of 12 reactions involving sequential loss of a, a, b, a, a, b, a, a, a, b, a, and b particles. Identify each intermediate nucleus and the final stable product nucleus.

Radon-222 decays by a series of three a emissions and two b emissions. What is the final stable nucleus?

One of the nuclides in spent nuclear fuel is U-235, an alpha emitter with a half-life of 703 million years. How long will it take for the amount of U-235 to reach 10.0% of its initial amount?

How many a particles and how many b particles are emitted in the 11-step decay of 235U into 207Pb?

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 g of aluminum-27? (The mass of an electron is given on the inside back cover.)

A radioactive sample contains 1.55 g of an isotope with a halflife of 3.8 days. What mass of the isotope remains after 5.5 days?

Naturally occurring uranium-238 undergoes a radioactive decay series and emits 8 a particles and 6 b particles. What is the stable nucleus at the end of the series?

A sample of F-18 has an initial decay rate of 1.5 * 105>s. How long will it take for the decay rate to fall to 2.5 * 103>s? (F-18 has a half-life of 1.83 hours.)

The half-life of indium-111, a radioisotope used in studying the distribution of white blood cells, is t1/2 = 2.805 days. What is the decay constant of 111In?

The atomic masses of nitrogen-14, titanium-48, and xenon-129 are 13.999234 amu, 47.935878 amu, and 128.904779 amu, respectively. For each isotope, calculate (a) the nuclear mass.

The decay constant of plutonium-239, a waste product from nuclear reactors, is 2.88 * 10-5 year - 1. What is the half-life of 239Pu?

Based on the following atomic mass values:1H, 1.00782 amu; 2H, 2.01410 amu; 3H, 3.01605 amu; 3He, 3.01603 amu; 4He, 4.00260 amu—and the mass of the neutron given in the text, calculate the energy released per mole in each of the following nuclear reactions, all of which are possibilities for a controlled fusion process: (b) 21H + 21H¡32He + 10n

Polonium-209, an a emitter, has a half-life of 102 years. How many alpha particles are emitted in 1.0 s from a 1.0 ng sample of 209Po?

A mammoth skeleton has a carbon-14 decay rate of 0.48 disintegration per minute per gram of carbon (0.48 dis>min # g C). When did the mammoth live? (Assume that living organisms have a carbon-14 decay rate of 15.3 dis>min # g C and that carbon- 14 has a half-life of 5715 yr.)

Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a half-life 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 NaI, in which only a small fraction of the iodide is radioactive. (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?

Why is it important that radioisotopes used as diagnostic tools in nuclear medicine produce gamma radiation when they decay? Why are alpha emitters not used as diagnostic tools?

Write the nuclear reaction for the neutron-induced fission of U-235 to form Xe-144 and Sr-90. How many neutrons are produced in the reaction?

Write the nuclear reaction for the neutron-induced fission of U-235 to produce Te-137 and Zr-97. How many neutrons are produced in the reaction?

A sample of 37Ar undergoes 8540 disintegrations/min initially but undergoes 6990 disintegrations/min after 10.0 days. What is the half-life of 37Ar in days?

Write the nuclear equation for the fusion of two H-2 atoms to form He-3 and one neutron.

Write the nuclear equation for the fusion of H-3 with H-1 to form He-4.

(c) What other substances are used as a moderator in nuclear reactor designs?

Radioactive decay exhibits a first-order rate law, rate = -∆N/∆t = kN, where N denotes the number of radio-active nuclei present at time t. The half-life of strontium-90, a dangerous nuclear fission product, is 29 years. (a) What fraction of the strontium-90 remains after three half-lives?

Complete and balance the nuclear equations for the following fission or fusion reactions: (a) 21H + 21H¡32He + _

Potassium ion, K+, is present in most foods and is an essen-tial nutrient in the human body. Potassium-40, however, which has a natural abundance of 0.0117%, is radioactive with t1/2 = 1.25 x 10^9 years. What is the decay constant of 40K? How many 40K+ ions are present in 1.00 g of KCl? How many disintegration/s does 1.00 g of KCl undergo?

Complete and balance the nuclear equations for the following fission reactions: (a) 23592U + 10n¡16062Sm + 7230Zn + _ 10n

The electronic systems on the New Horizons spacecraft, which launched on January 19, 2006, and reached its closest approach to Pluto on July 14, 2015, were powered by elec-tricity generated by heat. The heat came from the radioac-tive decay of 238Pu in the 11 kg of 238PuO2 fuel onboard. The generator provided 240 W when the spacecraft was launched. If the power output is directly proportional to the amount of 238Pu in the generator, what was the power output when the spacecraft reached Pluto? The half-life of 238Pu is 87.7 y.

The spent fuel elements from a fission reactor are much more intensely radioactive than the original fuel elements. (b) Given that only two or three neutrons are released per fission event and knowing that the nucleus undergoing fission has a neutron-to-proton ratio characteristic of a heavy nucleus, what sorts of decay would you expect to be dominant among the fission products?

If 1.0 g of matter is converted to energy, how much energy is formed?

A typical home uses approximately 1.0 * 103 kWh of energy per month. If the energy came from a nuclear reaction, what mass would have to be converted to energy per year to meet the energy needs of the home?

Which are classified as ionizing radiation: X rays, alpha particles, microwaves from a cell phone, and gamma rays?

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?

Calculate the quantity of energy produced per gram of U-235 (atomic mass = 235.043922 amu) for the neutron-induced fission of U-235 to form Xe-144 (atomic mass = 143.9385 amu) and Sr-90 (atomic mass = 89.907738 amu) (discussed in Problem 57).

Uranium-238 has a half-life of 4.47 * 109 years and decays through a series of events to yield lead-206. Estimate the age of a rock that contains 105 mmol of 238U and 33 mmol of 206Pb. Assume all the 206Pb is from the decay of 238U.

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?

The age of an igneous rock that has solidified from magma can be found by analyzing the amount of 40K and 40Ar. Potassium-40 emits a positron to produce argon-40 and the half-life of 40K is 1.25 * 109 years. What is the age of a rock whose 40Ar/40K ratio is 1.42?

A 75-kg human has a dose of 32.8 rad of radiation. How much energy is absorbed by the person's body? Compare this energy to the amount of energy absorbed by the person's body if he or she jumped from a chair to the floor (assume that the chair is 0.50 m from the ground and that all of the energy from the fall is absorbed by the person).

Chlorine has two stable nuclides, 35Cl and 37Cl. In contrast, 36Cl is a radioactive nuclide that decays by beta emission. (a) What is the product of decay of 36Cl?

Why does a given nucleus have less mass than the sum of its constituent protons and neutrons?

In an endothermic chemical reaction, do the products have more mass, less mass, or the same mass as the reactants? Explain.

Suppose a patient is given 1.55 mg of I-131, a beta emitter with a half-life of 8.0 days. Assuming that none of the I-131 is eliminated from the person's body in the first 4.0 hours of treatment, what is the exposure (in Ci) during those first four hours?

Complete each nuclear equation and calculate the energy change (in J>mol of reactant) associated with each (Be-9 = 9.012182 amu, Bi-209 = 208.980384 amu, He-4 = 4.002603 amu, Li-6 = 6.015122 amu, Ni-64 = 63.927969 amu, Rg-272 = 272.1535 amu, Ta-179 = 178.94593 amu, and W-179 = 178.94707 amu). a. _____ +94Be ¡63Li + 42He

What is the energy change ∆E (in kJ/mol) when an a particle is emitted from 174Ir? The atomic mass of 174Ir is 173.96666 the atomic mass of 170Re is 169.95804, and the atomic mass of a 4He atom is 4.00260.

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 typical nuclear reactor produces about 1.0 MW of power per day. What is the minimum rate of mass loss required to produce this much energy?

The radioactive isotope 100Tc decays to form the stable iso-tope 100Mo. (a) There are two possible pathways for this decay. Write balanced equations for both.

The radioactive isotope 100Tc decays to form the stable iso-tope 100Mo. (b) Only one of the pathways is observed. Calculate the energy released by both pathways, and explain why only one is observed. Relevant masses are: 100Tc = 99.907 657, 100Mo = 99.907 48, electron = 0.000 548 6.

Find the binding energy in an atom of 3He, which has a mass of 3.016030 amu.

Control rods in a nuclear reactor are often made of boron because it absorbs neutrons. Write the nuclear equation in which boron-10 absorbs a neutron to produce lithium-7 and an alpha particle.

What is the difference between uranium fuel rods in a nuclear power plant and uranium fuel for an atomic weapon?

The half-life of 238U is 4.5 * 109 yr. A sample of rock of mass 1.6 g produces 29 dis>s. Assuming all the radioactivity is due to 238U, find the percent by mass of 238U in the rock.

Can fuel rods in a power plant be used to make an atomic weapon without further treatment? Explain.

The half-life of 232Th is 1.4 * 1010 yr. Find the number of disintegrations per hour emitted by 1.0 mol of 232Th.

What are the benefits of using fusion over fission as a source of nuclear energy? Why have fusion reactors not been developed yet?

How much energy is released (in kJ) in the fusion reaction of 2H to yield 1 mol of 3He? The atomic mass of 2H is 2.0141, and the atomic mass of 3He is 3.0160.

How much energy (in kJ/mol) is produced in the following fission reaction of plutonium-239?

How much energy (in kJ/mol) is released in the fusion reaction with 2H and 3He?

How much energy (in kJ/mol) is released in the fusion reaction of 1H and 2H atoms?

The nuclide 18F decays by both electron capture and b+ decay. Find the difference in the energy released by these two processes. The atomic masses are 18F = 18.000950 and 18O = 17.9991598.

Balance the following equations for the nuclear fission of 235U. (b)

Balance the following equations for the nuclear fission of 235U. (a)

A 255-gram laboratory rat is exposed to 23.2 rads. How many grays did the rat receive? How many joules were absorbed by the rat?

The two most common isotopes of uranium are 235U and 238U. (d) 238U undergoes radioactive decay to 234Th. How many protons, electrons, and neutrons are gained or lost by the 238U atom during this process?

The maximum level of radon in drinking water is 4.0 pCi (4.0 x 10^-12Ci) per milliliter. (a) How many disintegrations occur per minute in 1 mL of water at the maximum radon level? (b) If the radioactive isotope is 222Rn(t1/2 = 3.8 days), how many 222Rn atoms are present in 1 mL of the water?

Nitrogen-16 is formed in the cooling water flowing through a hot reactor core in a nuclear power plant. It is formed when oxygen captures a neutron and then emits a b par-ticle. Determine the activity of 50.0 mg of 16N in units of Bq and Ci.

A proposed nuclear theory suggests that the relative abun-dances of the uranium isotopes 235U and 238U were approximately equal at the time they were formed. Today, the observed ratio of these isotopes is 7.25 x 10^-3. Give that the half-lives for radioactive decay are 7.04 x 19^8 are y for and 4.47 x 10^9 y for , calculate the age of the elements.

A small sample of wood from an archaeological site in Clo-vis, New Mexico, was burned in O2 and the CO2 produced was bubbled through a solution of Ba(OH)2 to produce a precipitation of BaCO3. When the BaCO3 was collected by filtration, a 1.000 g sample was found to have a radioactivity of 4.0 x 10^-5 Bq. The half-life of 14C is 5715 y, and living organisms have a radioactivity due to 14C if 15.3 disintegrations/min per gram of carbon. If the analysis was carried out in 1960, what is the date of the Clovis site?

Polonium-210, a naturally occurring radioisotope, is an alpha emitter, with t1/2=138 d. Assume that a sample fo 210Po with a mass of 0.700 mg was placed ina 250.0-mL flask, which was evacuated, sealed, and allowed to sit undisturbed. What would the pressure be inside the flask (in mmHg) at 20 degrees Celsius after 365 days if all the alpha particles emitted has become helium atoms?

Imagine that you have a 0.007 50 M aqueous MgCl2 solu-tion, prepared so that it contains a small amount of radio-active 28Mg. The half-life of 28Mg is 20.91 h, and the initial activity of the MgCl2 solution is 0.112 mCi>mL. Assume that 20.00 mL of this MgCl2 solution is added to 15.00 mL of 0.012 50 M aqueous Na2CO3 solution and that the resultant precipitate is then removed by filtration to yield a clear filtrate. After a long break to go for a run, you find that the activity of the filtrate measured 2.40 h after begin-ning the experiment is 0.029 mCi>mL. What are the molar concentrations of Mg2+ and CO32- in the filtrate, and what is the solubility product constant of MgCO3?