Question

a. Explain why the graphs of Figure 38.3 are mostly horizontal for ∆V > 0.

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

c. Explain the reasoning by which we claim that the stopping potential V_stop indicates the maximum kinetic energy of the electrons

Short answer

a) Further increase in the voltage cannot change the number of electrons arriving per second

b) Because there are a range of escape energies

c) The stopping potential measures the maximum kinetic energy by causing the most energetic electrons to turn back from the anode.

Step-by-step solution

Step 1. Questions based on basic concept of Quantization is given to us.

We need to provide relevant reasons for the given statements and Questions.

Step 2. Part a)

When $∆V$> 0, all the emitted electrons are attracted to and collected by the anode. This means a further increase in the voltage cannot change the number of electrons arriving per second and thus cannot increase the current.

Step 3. Part b)

The work function E₀ is the minimum energy an electron needs to escape from the metal. Some electrons, such as those a bit farther from the surface, need more than E₀, to escape.

Because there are a range of escape energies, the expelled electrons have a variety of kinetic energies rather than a single one.

Step 4. Part c)

If the anode potential is V, an electron leaving the cathode with kinetic energy K arrives at the anode with kinetic energy $K\text{'}=K+eV$. A negative V causes a decrease in kinetic energy. K' cannot become negative, so far $eV\le -K$ the anode repels the electron, causing it to return to the cathode. The emitted electrons have a maximum Kinetic energy K_max. When $eV=-K_{max}$, all electrons are turned back and current falls to zero.

If the current reaches zero at $V=-V_{stop}$then $V_{stop}=\frac{K_{max}}{e}.$The stopping potential measures the maximum kinetic energy by causing the most energetic electrons, those with $K=K_{max}$turns back from the anode.