1. A negatively charged electroscope can be discharged by shining an ultraviolet light on it. How does this happen?

2. You might think that an ultraviolet light shining on an initially uncharged electroscope would cause the electroscope to become positively charged as photoelectrons are emitted. In fact, ultraviolet light has no noticeable effect on an uncharged electroscope. Why not?

1. Explain why the graphs of Figure 38.3 are mostly horizontal for $\text{Δ}V>0$.

2. Explain why photoelectrons are ejected from the cathode with a range of kinetic energies, rather than all electrons having the same kinetic energy.

3. Explain the reasoning by which we claim that the stopping potential $V_{\text{stop}}$ indicates the maximum kinetic energy of the electrons.

How would the graph of Figure 38.2 look if classical physics provided the correct description of the photoelectric effect? Draw the graph and explain your reasoning. Assume that the light intensity remains constant as its frequency and wavelength are varied.

How would the graphs of Figure 38.3 look if classical physics provided the correct description of the photoelectric effect? Draw the graph and explain your reasoning. Include curves for both weak light and intense light.

FIGURE Q38.5 is the current-versus-potential-difference graph for a photoelectric-effect experiment with an unknown metal. How might the graph look if:

1. The light is replaced by a more intense light with the same wavelength. Draw it.

2. The metal is replaced by a different metal with a smaller work function? Draw it.

FIGURE Q38.5

Metal 1 has a larger work function than metal 2. Both are illuminated with the same short-wavelength ultraviolet light. Do photoelectrons from metal 1 have a higher speed, a lower speed, or the same speed as photoelectrons from metal 2? Explain.

Electron 1 is accelerated from rest through a potential difference of 100 V. Electron 2 is accelerated from rest through a potential difference of 200 V. Afterward, which electron has the larger de Broglie wavelength? Explain.

An electron and a proton are each accelerated from rest through a potential difference of 100 V. Afterward, which particle has the larger de Broglie wavelength? Explain.

FIGURE Q38.9 is a simulation of the electrons detected behind two closely spaced slits. Each bright dot represents one electron. How will this pattern change if

1. The electron-beam intensity is increased?

2. The electron speed is reduced?

3. The electrons are replaced by neutrons traveling at the same speed?

4. The left slit is closed?

FIGURE Q38.9

Your answers should consider the number of dots on the screen and the spacing, width, and positions of the fringes.

Imagine that the horizontal box of Figure 38.14 is instead oriented vertically. Also imagine the box to be on a neutron star where the gravitational field is so strong that the particle in the box slows significantly, nearly stopping, before it hits the top of the box. Make a qualitative sketch of the $n=3$ de Broglie standing wave of a particle in this box.

Hint: The nodes are not uniformly spaced.

If an electron is in a stationary state of an atom, is the electron at rest? If not, what does the term mean?

FIGURE Q38.12 shows the energy-level diagram of Element X.

1. What is the ionization energy of Element X?

2. An atom in the ground state absorbs a photon, then emits a photon with a wavelength of 1240 nm. What was the energy of the photon that was absorbed?

3. An atom in the ground state has a collision with an electron, then emits a photon with a wavelength of 1240 nm. What conclusion can you draw about the initial kinetic energy of the electron?

FIGURE Q38.12