The Photoelectric Effect — Question 7

Question 7

A two-color photocurrent has a cutoff set by its most energetic photons

A cathode of work function 2.00 eV receives equal incident photon rates $\dot N$ at 310 nm and 400 nm. Each color has the same external yield $\eta$. Ignore offsets and space charge. Use $hc=1240\,\mathrm{eV\,nm}$, $e=1.60\times10^{-19}\,\mathrm C$, and $eV_s=K_{\max}=hf-\phi$ when emission is allowed.

1. Find the two maximum electron energies and the overall stopping voltage.

2. If a filter removes the 310 nm photons, find the changes in saturation current and stopping voltage.

Question 7 - Solution

A two-color photocurrent has a cutoff set by its most energetic photons

(a) Method and calculation

$$K_{310}=4.00-2.00=\boxed{2.00\,\mathrm{eV}},\quad K_{400}=3.10-2.00=\boxed{1.10\,\mathrm{eV}}.$$$$\boxed{V_s=2.00\,\mathrm V},\qquad I_{\mathrm{sat}}=2e\eta\dot N.$$

(b) Interpretation and further calculation

$$\boxed{I_{\mathrm{sat,filtered}}=e\eta\dot N=I_{\mathrm{sat}}/2}.$$$$\boxed{V_{s,\mathrm{filtered}}=1.10\,\mathrm V}.$$

Physical check

The cutoff is determined by the highest emitted kinetic energy, not the mean photon energy.