The Photoelectric Effect — Question 1

Question 1

A stopping potential and a threshold wavelength encode the same work function

A surface with work function $\phi=2.20\,\mathrm{eV}$ is illuminated at 310 nm. 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 maximum electron kinetic energy and stopping potential.

2. Find the threshold wavelength and decide whether 620 nm light can cause single-photon emission.

Question 1 - Solution

A stopping potential and a threshold wavelength encode the same work function

(a) Method and calculation

$$E_\gamma=1240/310=4.00\,\mathrm{eV},\quad\boxed{K_{\max}=1.80\,\mathrm{eV}}.$$$$\boxed{V_s=1.80\,\mathrm V}.$$

(b) Interpretation and further calculation

$$\boxed{\lambda_0=hc/\phi=563.636\,\mathrm{nm}}.$$$$E_{620}=2.00\,\mathrm{eV}<\phi\quad\Rightarrow\quad\boxed{\text{no single-photon emission}}.$$

Physical check

A negative formal kinetic energy signals forbidden emission; it is not an emitted electron with negative kinetic energy.