In an experiment done in a laboratory on the earth, the wavelength of light emitted by a hydrogen atom in the $n=4$ to $n=2$ transition is $486.1$ nm. In the light emitted by the quasar 3C273 (see Problem $36.60$), this spectral line is redshifted to $563.9$ nm. Assume the redshift is described by Eq. ($44.14$) and use the Hubble law to calculate the distance in light-years of this quasar from the earth.

A photon has momentum of magnitude $8.24\times {10}^{-28}$ kg-m/s. What is the energy of this photon? Give your answer in joules and in electron volts.

In a nuclear physics experiment, a proton is fired toward a Z = 13 nucleus with the diameter and neutron energy levels shown in Figure 40.17. The nucleus, which was initially in its ground state, subsequently emits a gamma ray with wavelength 1.73×10⁻⁴ nm. What was the minimum initial speed of the proton? Hint: Don't neglect the proton-nucleus collision.

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

A $67$-kg person accidentally ingests $0.35$ Ci of tritium.

(a) Assume that the tritium spreads uniformly throughout the body and that each decay leads on the average to the absorption of $5.0$ keV of energy from the electrons emitted in the decay. The half-life of tritium is $12.3$ y, and the RBE of the electrons is $1.0$. Calculate the absorbed dose in rad and the equivalent dose in rem during one week.

(b) The ${\beta }^{-}$ decay of tritium releases more than $5.0$ keV of energy. Why is the average energy absorbed less than the total energy released in the decay?

FIGURE P39.31 shows the wave function of a particle confined between x = 0 nm and x = 1.0 nm. The wave function is zero outside this region. Determine the value of the constant c, as defined in the figure.

In most metals, the atomic ions form a regular arrangement called a crystal lattice. The conduction electrons in the sea of electrons move through this lattice. FIGURE P40.34 is a one-dimensional model of a crystal lattice. The ions have mass m, charge e, and an equilibrium separation b. What wavelength photons are emitted during quantum jumps between adjacent energy levels? Is this wavelength in the infrared, visible, or ultraviolet portion of the spectrum?

A ²²²Rn atom (radon) in a 0.75 T magnetic field undergoes radioactive decay, emitting an alpha particle in a direction perpendicular to $\overrightarrow{B}$. The alpha particle begins cyclotron motion with a radius of 45 cm. With what energy, in MeV, was the alpha particle emitted?

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