Chapter 20

State the following: (a) the law of conservation of mass-energy (b) the Einstein equation

Why isn't the sum of the masses of all nucleons in one nucleus equal to the mass of the actual nucleus?

When a substance is described as radioactive, what does that mean? Why is the term radioactive decay used to describe the phenomenon?

Three kinds of radiation make up nearly all of the radiation observed from naturally occurring radionuclides. What are they?

Give the composition of each of the following: (a) alpha particle, (b) beta particle, (c) positron, (d) deuteron.

Why is the penetrating ability of alpha radiation less than that of beta or gamma radiation?

With respect to their formation, how do gamma rays and X rays differ?

For the process of beta emission, where does the electron originate? What particle emits the electron and what else is formed?

Lanthanum-139 is a stable nuclide but lanthanum-140 is unstable \(\left(t_{1 / 2}=40 \mathrm{hr}\right)\). What rule of thumb concerning nuclear stability is involved?

As the atomic number increases, the neutron/proton ratio increases. What does this suggest is a factor in nuclear stability?

What decay particle is emitted from a nucleus of low to intermediate atomic number but a relatively high neutron/proton ratio? How does the emission of this particle benefit the nucleus?

What decay particle is emitted from a nucleus of low to intermediate atomic number but a relatively low neutron/proton ratio? How does the emission of this particle benefit the nucleus?

Rutherford theorized that a compound nucleus forms when helium nuclei hit nitrogen- 14 nuclei. If this compound nucleus decayed by the loss of a neutron instead of a proton, what would be the other product?

Why is it easier to use neutrons to form compound nuclei rather than alpha particles or other nuclei?

What specific property of nuclear radiation is used by the Geiger counter?

What units, SI and common, are used to describe each of the following? (a) the activity of a radioactive sample (b) the energy of a particle or of a photon of radiation given off by a nucleus (c) the amount of energy absorbed by a given mass by a dose of radiation (d) dose equivalents for comparing biological effects

Why should a radionuclide used in medical diagnostic procedures have a short half-life? If the half-life is too short, what problem arises?

In general terms, explain how neutron activation analysis is used and how it works.

What is one assumption in the use of the uranium/lead ratio for dating ancient geologic formations?

List some of the kinds of radiation that make up our background radiation.

What do each of the following terms mean? (a) thermal neutron, (b) nuclear fission, (c) fissile isotope, (d) nuclear fusion, (e) critical mass

Which fissile isotope occurs in nature?

What fact about the fission of uranium-235 makes it possible for a chain reaction to occur?

Explain in general terms why fission generates more neutrons than needed to initiate it.

What purpose is served by a moderator in a nuclear reactor?

Why is there no possibility of an atomic bomb-type explosion from a nuclear power plant?

Calculate the velocity, relative to us, in \(\mathrm{m} \mathrm{s}^{-1}\) of an object with a rest mass, \(m_{0},\) of \(1.000 \mathrm{~kg}\) when its mass, \(m,\) is (a) \(1.005 \mathrm{~kg}\), (b) \(1.1 \mathrm{~kg},\) and (c) \(5.0 \mathrm{~kg}\).

Calculate the mass equivalent in grams of \(1.00 \mathrm{~kJ}\) of energy.

Calculate the energy equivalent in \(\mathrm{kJ}\) of \(1.00 \mathrm{~g}\) of mass.

Show that the mass equivalent of the energy released by the complete combustion of \(1 \mathrm{~mol}\) of methane \((890 \mathrm{~kJ})\) is \(9.89 \mathrm{ng}\).

Write the balanced nuclear equation for each of the following nuclear reactions: (a) electron capture by iron-55, (b) beta emission by potassium-42, (c) positron emission by ruthenium-93, (d) alpha emission by californium- 251 .

Write the symbols, including the atomic and mass numbers, for the radionuclides that would give each of the following products: (a) fermium- 257 by alpha emission, (b) bismuth- 211 by beta emission, (c) neodymium- 141 by positron emission, (d) tantalum-179 by electron capture.

Each of the following nuclides forms by the decay mode described. Write the symbols of the parents, giving both atomic and mass numbers: (a) rubidium- 80 formed by electron capture, (b) antimony-121 formed by beta emission, (c) chromium- 50 formed by positron emission, (d) californium- 253 formed by alpha emission.

Write the symbol of the nuclide that forms from cobalt- 58 when it decays by electron capture.

If we begin with \(3.00 \mathrm{mg}\) of iodine- \(131\left(t_{1 / 2}=8.07 \mathrm{hr}\right)\), how much remains after six half-life periods?

A sample of technetium- \(99 m\) with a mass of \(9.00 \mathrm{ng}\) will have decayed to how much of this radionuclide after four half-life periods (about 1 day)?

When vanadium- 51 captures a deuteron \(\left({ }_{1}^{2} \mathrm{H}\right),\) what compound nucleus forms? (Write its symbol.) This particle expels a proton \(\left({ }_{1}^{1} p\right) .\) Write the balanced nuclear equation for the overall change from vanadium- 51 .

Gamma-ray bombardment of bromine-81 causes a transmutation in which a neutron is one product. Write the symbol of the other product.

Neutron bombardment of cadmium-115 results in neutron capture and the release of gamma radiation. Write the balanced nuclear equation.

Suppose that a radiologist who is \(2.0 \mathrm{~m}\) from a small, unshielded source of radiation receives 2.8 units of radiation. To reduce the exposure to 0.28 units of radiation, to what distance from the source should the radiologist move?

A sample giving \(3.7 \times 10^{10}\) disintegrations per second has what activity in \(\mathrm{Ci}\) and in \(\mathrm{Bq}\) ?

A sample of a radioactive metal used in medicine has an activity of \(3.5 \mathrm{mCi}\). What is its activity in \(\mathrm{Bq}\) and how many disintegrations/s does it give?

Iodine- 131 is a radioisotope present in radioactive fallout that targets the thyroid gland. If \(1.00 \mathrm{mg}\) of \({ }^{131} \mathrm{I}\) has an activity of \(4.6 \times 10^{12} \mathrm{~Bq}\), what is the decay constant for 131 I? What is the half-life, in seconds?

What percentage of cesium chloride made from cesium137 (beta emitter, \(t_{1 / 2}=30.1 \mathrm{y}\) ) remains after \(150 \mathrm{y}\) ? What chemical product forms?

A worker in a laboratory unknowingly became exposed to a sample of radio- labeled sodium iodide made from iodine- 131 (beta emitter, \(t_{1 / 2}=8.07\) day). The mistake was realized 28.0 days after the accidental exposure, at which time the activity of the sample was \(25.6 \times 10^{-5} \mathrm{Ci} / \mathrm{g} .\) The safety officer needed to know how active the sample was at the time of the exposure. Calculate this value in \(\mathrm{Ci} / \mathrm{g}\).

Technetium- \(99 \mathrm{~m}\) (gamma emitter, \(t_{1 / 2}=6.02 \mathrm{hr}\) ) is widely used for diagnosis in medicine. A sample prepared in the early morning for use that day had an activity of \(4.52 \times 10^{-6} \mathrm{Ci}\). What will its activity be at the end of the day- that is, after \(8.00 \mathrm{hr}\) ?

What is the balanced nuclear equation for each of the following changes? (a) beta emission from aluminum- 30 , (b) alpha emission from einsteinium-252, (c) electron capture by molybdenum-93, (d) positron emission by phosphorus- 28

Give the balanced nuclear equation for each of the following changes: (a) positron emission by carbon-10, (b) alpha emission by curium- 243 , (c) electron capture by vanadium- \(49,\) (d) beta emission by oxygen-20.

If a positron is to be emitted spontaneously, how much more mass (as a minimum) must an atom of the parent have than an atom of the daughter nuclide? Explain.

\({ }^{15} \mathrm{O}\) decays by positron emission with a half-life of 124 s. (a) Give the proper symbol of the product of the decay. (b) How much of a \(750 \mathrm{mg}\) sample of \({ }^{15} \mathrm{O}\) remains after 5.0 min of decay? (Contributed by Prof. W. J. Wysochansky, Georgia Southern University.)