Download Chapter 29: Atomic Physics

Chapter 29: Atomic Physics
1. How many possible subshells are there for the n = 4 level of hydrogen? (a) 5 (b) 4 (c)
3 (d) 2 (e) 1
Answer: (b). The number of subshells is the same as the number of allowed values of ℓ.
The allowed values of ℓ for n = 4 are ℓ = 0, 1, 2, and 3, so there are four subshells.
2. When the principal quantum number is n = 5, how many different values of (a) ℓ and
(b) mℓ are possible?
Answer: (a) Five values (0, 1, 2, 3, 4) of ℓ and (b) nine different values (−4, −3, −2, −1,
0, 1, 2, 3, 4) of mℓ as follows:
ℓ
0
1
2
3
4
mℓ
0
−1, 0, 1
−2, −1, 0, 1, 2
−3, −2, −1, 0, 1, 2, 3
−4, −3, −2, −1, 0, 1, 2, 3, 4
3. Sketch a vector model (shown in Fig. 29.7 for ℓ = 2) for ℓ = 1.

Figure 29.7 A vector model for ℓ = 2. (a) The allowed projections of the orbital angular momentum L

relative to a magnetic field that defines the z direction. (b) The orbital angular momentum vector L lies on
the surface of a cone.
Answer: The vector model for ℓ = 1 is shown below.
4. Rank the energy necessary to remove the outermost electron from the following three
elements, smallest to largest: lithium, potassium, cesium.
Answer: Cesium, potassium, lithium. The higher the value of Z, the closer to zero is the
energy associated with the outermost electron and the smaller is the ionization energy.
5. What are the initial and final shells for an Mβ line in an x-ray spectrum?
Answer: Final: M. Initial: O (because the subscript β indicates that the initial shell is the
second shell higher than M).
6. In an x-ray tube, as you increase the energy of the electrons striking the metal target,
(i) the wavelengths of the characteristic x-rays (a) increase, (b) decrease, or (c) do not
change and (ii), the minimum wavelength of the bremsstrahlung (a) increases, (b)
decreases, or (c) does not change.
Answer: (i), (c). The wavelengths of the characteristic x-rays are determined by the
separation between energy levels in the atoms of the target, which is unrelated to the
energy with which electrons are fired at the target. The only dependence is that the
incoming electrons must have enough energy to eject an atomic electron from an inner
shell. (ii), (b). The minimum wavelength of the bremsstrahlung is associated with the
highest-energy photon. This photon comes from an electron striking the target and giving
up all its energy to electromagnetic radiation in one collision. Therefore, higher-energy
incoming electrons will result in higher-energy photons with shorter wavelengths.