The Photoelectric Effect — Question 9

Question 9

A classical accumulation estimate predicts a long delay under a stated microscopic model

A hypothetical classical model assigns one electron an effective collecting area $a=10^{-20}\,\mathrm m^2$ under intensity $\mathcal I=10^{-3}\,\mathrm{W/m^2}$. It must accumulate work function energy $\phi=2.00\,\mathrm{eV}$ before emission. Take $1\,\mathrm{eV}=1.60\times10^{-19}\,\mathrm J$.

1. Calculate the accumulation time predicted by this model.

2. Contrast its inverse-intensity dependence with one-photon energy transfer when $hf>\phi$.

Question 9 - Solution

A classical accumulation estimate predicts a long delay under a stated microscopic model

(a) Method and calculation

$$P_e=\mathcal I a=10^{-23}\,\mathrm W,\qquad\phi=3.20\times10^{-19}\,\mathrm J.$$$$\boxed{t_{\mathrm{acc}}=\phi/(\mathcal I a)=3.20\times10^4\,\mathrm s}.$$

(b) Interpretation and further calculation

$$t_{\mathrm{acc}}\propto\mathcal I^{-1}.$$$$\text{One absorption:}\quad hf\ge\phi,\qquad K_{\max}=hf-\phi.$$

Physical check

Photon absorption does not require gradual accumulation from many weak cycles. This does not imply every microscopic response or photon waiting time is literally zero.