Chapter Questions
Do gravitational forces play a significant role in atomic structure? Explain.
What are the most significant differences between the Bohr model of the hydrogen atom and the Schrodinger analysis? What are the similarities?
For a body orbiting the sun, such as u planet, comet, of asteroid, is there any restriction on the z-component of its orbital angular momentum such as there is with the z-component of the electron's orbital angular momentum in hydrogen? Explain.
Why is the analysis of the helium atom much more complex than that of the hydrogen atom, either in a Bohr type of mode or using the Schrodinger equation?
The Stem-Gerlach experiment is always performed with beams of neutral atoms. Wouldn't it be easier to form beams using Ionized atoms? Why won't this work?
(a) If two electrons in hydrogen atoms hive the same principal quantum number, can they have different orbital angular momentum? How? (b) If two electrons in hydrogen atoms have the same orbital angular-momentum quantum number, can they have they have different principal quantum numbers? How?
In the Stern-Gertach experiment, why is it essential for the magnetic field to be inhomogeneous (that is, nonuniform)?
In the ground state of the helium atom one electron must have "spin down" and the other "spin up." Why?
An electron in u hydrogen atom is in an s level, and the atom is in a magnetic field $\vec{B}=B \bar{k}$. Explain why the "spin up" state $\left(m_{s}=+\frac{1}{2}\right)$ has a higher energy than the "spin down" state $\left(m_{4}=-\frac{1}{4}\right)$.
The central field approximation is more accurate for alkali metals than for transition metals such $\mathrm{Bs}$ iron, nickel, or copper. Why?
Table $41.3$ shows that for the ground state of the potassium atom, the outermost electron is in a 4s state. What does this tell you about the relative energies of the $3 d$ and $4 s$ levels for this atom? Explain.
A student asserted that any filled shell must have zero total? angular momentum and hence mast be spherically symmetric. Do you believe this is true? What about a filled sub-shell? Explain.
Why do the transition elements $(Z=21$ to 30$)$ all have similar chemical properties?
Use Table 41. 3 to help determine the ground-state electron configuration of the neutral gallium atom (Ga) as well as the ions Gat and $\mathrm{Ga}^{-}$. Gallium has an atomic number of 31 .
On the basis of the Pauli exclusion principle, the structure of the periodic table of the elements shows that there must be a fourth quantum number in addition to $n, l$, and $m_{p}$. Explain.
A small amount of magnetic-field splitting of spectral lines occurs even when the atoms are not in a magnetic field. What causes this?
The ionization energies of the alkali metals (that is, the lowest energy required to remove one outer electron when the atom is in its ground state) are about 4 or $5 \mathrm{eV}$, while those of the noble gases are in the range from 11 to $25 \mathrm{eV}$. Why is there difference?
The energy required to remove the 3 s electron from a sodium atom in its ground state is about $5 \mathrm{cV}$. Would you expect the energy required to remove an additional electron to be about the same, or more, or less? Why?
What is the "central-field approximation"' and why is it only an approximation?
The nucleus of n gold atom contains 79 protons. How does the energy required to remove a 1s electron completely from a gold atom compare with the energy required to remove the electron from the ground level in a hydrogen atom? In what region of the electromagnetic spectrum would a photon with this energy for each of these two atoms lie?
What is the basic distinction between x-ray energy levels and ordinary energy levels?
An atom in its ground level absorbs a photon with energy equal to the $K$ absorption edge. Does absorbing this photon ionize this atom? Explain.
Can a hydrogen atom emit $x$ rays? If so, how? if not, why not?