Consider the three hydrogen-atom states $6p$, $5d$, and $4f$. Which has the highest energy?

What is the difference between the probability density and the radial probability density?

What is the difference between $l$ and $L$?

What is the difference between $s$ and $S$?

FIGURE Q41.5 shows the outcome of a Stern-Gerlach experiment with atoms of element X.

1. Do the peaks represent different values of the atom’s total angular momentum or different values of the $z$-component of its angular momentum? Explain.

2. What angular momentum quantum numbers characterize these four peaks?

FIGURE Q41.5

Does each of the configurations in FIGURE Q41.6 represent a possible electron configuration of an element? If so, (i) identify the element and (ii) determine whether this is the ground state or an excited state. If not, why not?

FIGURE Q41.6

What is an atom’s ionization energy? In other words, if you know the ionization energy of an atom, what is it that you know about the atom?

Figure 41.22 shows that the ionization energy of cadmium $(Z=48)$ is larger than that of its neighbors. Why is this?

A neon discharge tube emits a bright reddish-orange spectrum, but a glass tube filled with neon is completely transparent. Why doesn’t the neon in the tube absorb orange and red wavelengths?

The hydrogen atom $1s$ wave function is a maximum at $r=0$. But the $1s$ radial probability density, shown in Figure 41.7, peaks at $r=a_{\text{B}}$ and is zero at $r=0$. Explain this paradox.

In a multielectron atom, the lowest-$l$ state for each $n$ ($2s$, $3s$, $4s$, etc.) is significantly lower in energy than the hydrogen state having the same $n$. But the highest-$l$ state for each $n$ ($2p$, $3d$, $4f$, etc.) is very nearly equal in energy to the hydrogen state with the same $n$. Explain.

In FIGURE Q41.12, a photon with energy 2.0 eV is incident on an atom in the $p$ state. Does the atom undergo an absorption transition, a stimulated emission transition, or neither? Explain.

FIGURE Q41.12