Calculate the nuclear diameters of (a) ⁴He, (b) ⁵⁶Fe, and (c) ²³⁸U.

Which stable nuclei have a diameter of 7.46 fm?

Calculate (in MeV) the total binding energy and the binding energy per nucleon for ¹²⁹I and for ¹²⁹Xe.

Use the potential-energy diagram in Figure 42.8 to estimate the ratio of the gravitational potential energy to the nuclear potential energy for two neutrons separated by 1.0 fm.

Draw energy-level diagrams, similar to Figure 42.11, for all A = 14 nuclei listed in Appendix C. Show all the occupied neutron and proton levels.

A Geiger counter is used to measure the decay of a radioactive isotope produced in a nuclear reactor. Initially, when the sample is first removed from the reactor, the Geiger counter registers 15,000 decays/s. 15 h later the count is down to 5500 decays/s. At what time after the sample's removal from the reactor is the count 1200 decays/s?

A sample of 1.0 x 10¹⁰ atoms that decay by alpha emission has a half-life of 100 min. How many alpha particles are emitted between t = 50 min and t = 200 min?

The radioactive isotope ²³⁰Th has a density of 11,700 kg/m³ and a half-life of 75,000 yr. What is the radius of a ²³⁰Th sphere that has an activity of 1.0 Ci?

Identify the unknown isotope $X$ in the following decays. ${}^7\text{Be}+{\text{e}}^{-}\to \text{X}+\nu$

Identify the unknown isotope $X$ in the following decays. $\text{X}{\to }^{40}\text{K}+{\text{e}}^{+}+\nu$

For those that are not stable, identify both the decay mode and the daughter nucleus.

An unstable nucleus undergoes alpha decay with the release of 5.52 MeV of energy. The combined mass of the parent and daughter nuclei is 452 u. What was the mass number of the parent nucleus?

What is the total energy (in MeV) released in the beta-minus decay of ³H?

The doctors planning a radiation therapy treatment have determined that a 100 g tumor needs to receive 0.20 J of gamma radiation. What is the dose in grays?

A 50 kg laboratory worker is exposed to 20 mJ of beta radiation. What is the dose equivalent in mrem?

Particle accelerators fire protons at target nuclei so that investigators can study the nuclear reactions that occur. In one experiment, the proton needs to have 20 MeV of kinetic energy as it impacts a ²⁰⁷Pb nucleus. With what initial kinetic energy (in MeV) must the proton be fired toward the lead target? Assume the nucleus stays at rest. Hint: The proton is not a point particle.

You learned in Chapter 41 that the binding energy of the electron in a hydrogen atom is 13.6 eV. By how much does the mass decrease when a hydrogen atom is formed from a proton and an electron? Give your answer both in atomic mass units and as a percentage of the mass of the hydrogen atom.

Use the graph of binding energy to estimate the total energy released if three ⁴He nuclei fuse together to form a ¹²C nucleus.

What energy (in MeV) alpha particle has a de Broglie wavelength equal to the diameter of a ²³⁸U nucleus?

What is the age in years of a bone in which the ¹⁴C/¹²C ratio is measured to be 1.65 x 10⁻¹³?

The radium isotope ²²³Ra, an alpha emitter, has a half-life of 11.43 days. You happen to have a 1.0 g cube of ²²³Ra, so you decide to use it to boil water for tea. You fill a well-insulated container with 100 mL of water at 18℃ and drop in the cube of radium. How long will it take the water to boil?

A sample contains radioactive atoms of two types, A and B. Initially there are five times as many A atoms as there are B atoms. Two hours later, the numbers of the two atoms are equal. The half-life of A is 0.50 hour. What is the half-life of B?

There is evidence that low-energy x rays have an RBE slightly greater than 1. Suppose that 10 keV photons with an RBE of 1.2 are used to make a chest x ray. A 60 kg person receives a 0.30 mSv dose from a chest x ray that exposes 25% of the patient's body. How many x ray photons are absorbed in the patient's body?

All the very heavy atoms found in the earth were created long ago by nuclear fusion reactions in a supernova, an exploding star. The debris spewed out by the supernova later coalesced into the gases from which the sun and the planets of our solar system were formed. Nuclear physics suggests that the uranium isotopes ²³⁵U and ²³⁸U should have been created in roughly equal numbers. Today, 99.28% of uranium is ²³⁸U and only 0.72% is ²³⁵U. How long ago did the supernova occur?

It might seem strange that in beta decay the positive proton, which is repelled by the positive nucleus, remains in the nucleus while the negative electron, which is attracted to the nucleus, is ejected. To understand beta decay, let's analyze the decay of a free neutron that is at rest in the laboratory. We'll ignore the antineutrino and consider the decay n → p⁺ + e⁻. The analysis requires the use of relativistic energy and momentum, from Chapter 36. What is the total kinetic energy, in MeV, of the proton and electron?

It might seem strange that in beta decay the positive proton, which is repelled by the positive nucleus, remains in the nucleus while the negative electron, which is attracted to the nucleus, is ejected. To understand beta decay, let's analyze the decay of a free neutron that is at rest in the laboratory. We'll ignore the antineutrino and consider the decay n → p⁺ + e⁻. The analysis requires the use of relativistic energy and momentum, from Chapter 36. Write the equation that expresses the conservation of relativistic energy for this decay. Your equation will be in terms of the three masses m_n, m_p and m_e and the relativistic factors y_p and y_e.

It might seem strange that in beta decay the positive proton, which is repelled by the positive nucleus, remains in the nucleus while the negative electron, which is attracted to the nucleus, is ejected. To understand beta decay, let's analyze the decay of a free neutron that is at rest in the laboratory. We'll ignore the antineutrino and consider the decay n → p⁺ + e⁻. The analysis requires the use of relativistic energy and momentum, from Chapter 36. Write the equation that expresses the conservation of relativistic momentum for this decay. Let v represent speed, rather than velocity, then write any minus signs explicitly.