0. Math Review

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.

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. $\text{X}{\to }^{40}\text{K}+{\text{e}}^{+}+\nu$

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.

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?

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?

The oxygen nucleus ¹⁶O has a radius of 3.0 fm. With what speed must a proton be fired toward an oxygen nucleus to have a turning point 1.0 fm from the surface? Assume the nucleus remains at rest.

At what speed is an electron’s de Broglie wavelength (a) 1.0 nm, (b) 1.0 μm, and (c) 1.0 mm?

The allowed energies of a simple atom are 0.00 eV, 4.00 eV, and 6.00 eV. Draw the atom’s energy-level diagram. Label each level with the energy and the quantum number.