(a) If you treat an electron as a classical spherical object with a radius of 1.0 * 10-17 m, what angular speed is necessary to produce a spin angular momentum of magnitude 23 4 U? (b) Use v = rv and the result of part (a) to calculate the speed v of a point at the electron's equator. What does your result suggest about the validity of this model?

The 5s electron in rubidium (Rb) sees an effective charge of 2.771e. Calculate the ionization energy of this electron.

A hydrogen atom in a particular orbital angular momentum state is found to have j quantum numbers 7 2 and 9 2 . (b) If n = 5, what is the energy difference between the j = 7 2 and j = 9 2 levels?

Calculate the energy difference between the ms = 1 2 ('spin up') and ms = - 1 2 ('spin down') levels of a hydrogen atom in the 1s state when it is placed in a 1.45-T magnetic field in the negative z@direction. Which level, ms = 1 2 or ms = - 1 2 , has the lower energy?

The hyperfine interaction in a hydrogen atom between the magnetic dipole moment of the proton and the spin magnetic dipole moment of the electron splits the ground level into two levels separated by 5.9 * 10-6 eV. (a) Calculate the wavelength and frequency of the photon emitted when the atom makes a transition between these states, and compare your answer to the value given at the end of Section 41.5. In what part of the electromagnetic spectrum does this lie? Such photons are emitted by cold hydrogen clouds in interstellar space; by detecting these photons, astronomers can learn about the number and density of such clouds.

A hydrogen atom in the 5g state is placed in a magnetic field of 0.600 T that is in the z@direction. (a) Into how many levels is this state split by the interaction of the atom's orbital magnetic dipole moment with the magnetic field?

A hydrogen atom in a 3p state is placed in a uniform external magnetic field B S . Consider the interaction of the magnetic field with the atom's orbital magnetic dipole moment. (a) What field magnitude B is required to split the 3p state into multiple levels with an energy difference of 2.71 * 10-5 eV between adjacent levels?

Pure germanium has a band gap of 0.67 eV. The Fermi energy is in the middle of the gap. (a) For temperatures of 250 K, 300 K, and 350 K, calculate the probability f(E) that a state at the bottom of the conduction band is occupied.

At the Fermi temperature T_F, E_F = kT_F (see Exercise 42.22). When T = T_F, what is the probability that a state with energy E = 2E_F is occupied?