91Ó°ÊÓ

For a hydrogen atom in the ground state, find the total energy, the potential energy, and the electron's kinetic energy. Verify that \(E=K+U\)

Find the minimum quantum number needed to make a hydrogen atom at least \(0.50 \mu \mathrm{m}\) in diameter.

A hydrogen atom in the \(n=5\) state drops to the \(n=2\) state by undergoing two downward transitions. What are all possible combinations of the resulting photon wavelengths?

Find the ground-state energies of (a) \(\mathrm{He}^{+}\); (b) \(\mathrm{Li}^{2+}\).

Consider the spectrum of \(\mathrm{He}^{+}\) resulting from downward transitions to the \(n=4\) level. (a) What wavelength results when initially \(n=6 ?\) (b) To which transition in hydrogen does that wavelength correspond? (c) What transitions (initial \(n\) to final \(n\) ) in \(\mathrm{He}^{+}\) produce the rest of the wavelengths seen in hydrogen's Balmer series?

Give spectroscopic notation for each of these electron states: (a) \(n=2, l=0\) (b) \(n=4, l=1\) (c) \(n=4, l=3\) (d) \(n=3\), \(l=2\)

For each of the following electronic states in hydrogen, find the magnitudes of the orbital and spin angular momenta: (a) \(3 s\) (b) \(3 p\) (c) \(3 d\).

For an electron in the \(3 p\) state of hydrogen, calculate all allowed values of (a) orbital angular momentum; (b) z-component of orbital angular momentum; (c) z-component of spin angular momentum.

A hydrogen atom has energy \(-1.36 \times 10^{-19} \mathrm{~J},\) and the electron can be in any one of 10 different quantum states. Find the spectroscopic notation for this atom.

By what factor does a hydrogen atom's angular momentum change when it makes the following transitions: (a) \(3 d\) to \(2 p\) (b) \(3 p\) to \(4 d ;\) (c) \(4 f\) to \(3 d\) ?