35. Special Relativity

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

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?

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?

To initiate a nuclear reaction, an experimental nuclear physicist wants to shoot a proton into a 5.50-fm-diameter ¹²C nucleus. The proton must impact the nucleus with a kinetic energy of 3.00 MeV. Assume the nucleus remains at rest. Through what potential difference must the proton be accelerated from rest to acquire this speed?

A typical electron in a piece of metallic sodium has energy −E₀ compared to a free electron, where E₀ is the 2.36 eV work function of sodium. At what distance beyond the surface of the metal is the electron’s probability density 10% of its value at the surface?

What is the wavelength, in nm, of a photon with energy (a) 0.30 eV, (b) 3.0 eV, and (c) 30 eV? For each, is this wavelength visible, ultraviolet, or infrared light?

What is the energy, in keV, of 75 keV x-ray photons that are backscattered (i.e., scattered directly back toward the source) by the electrons in a target?

55 keV x-ray photons are incident on a target. At what scattering angle do the scattered photons have an energy of 50 keV?

The allowed energies of a simple atom are 0.00 eV, 4.00 eV, and 6.00 eV. An electron traveling with a speed of 1.30×10⁶ m/s collides with the atom. Can the electron excite the atom to the n = 2 stationary state? The n = 3 stationary state? Explain.

What quantum number of the hydrogen atom comes closest to giving a 100-nm-diameter electron orbit?

Find the radius of the electron’s orbit, the electron’s speed, and the energy of the atom for the first three stationary states of He+.

The cosmic microwave background radiation is light left over from the Big Bang that has been Doppler-shifted to microwave frequencies by the expansion of the universe. It now fills the universe with 450 photons/cm³ at an average frequency of 160 GHz. How much energy from the cosmic microwave background, in MeV, fills a small apartment that has 95 m² of floor space and 2.5-m-high ceilings?

An electron confined in a one-dimensional box is observed, at different times, to have energies of 12 eV, 27 eV, and 48 eV. What is the length of the box?

A muon—a subatomic particle with charge −e and a mass 207 times that of an electron—is confined in a 15-pm-long, one-dimensional box. ( 1pm=1picometer=10⁻¹² m.) What is the wavelength, in nm, of the photon emitted in a quantum jump from n = 2 to n = 1?