The Photoelectric Effect — Question 10

Question 10

A specified multiphoton channel changes the intensity scaling and threshold

An intense source supplies 2.00 eV photons to a surface with work function 4.50 eV. Assume an allowed n-photon channel transfers $nhf$ to one electron, with emission rate proportional to $\mathcal I^n$ in the weak, unsaturated limit for that channel.

1. Find the smallest allowed n and its maximum electron kinetic energy.

2. Find the predicted rate multiplier when intensity doubles and explain why this is outside the single-photon model.

Question 10 - Solution

A specified multiphoton channel changes the intensity scaling and threshold

(a) Method and calculation

$$nhf\ge\phi\quad\Rightarrow\quad n\ge4.50/2.00=2.25.$$$$\boxed{n_{\min}=3},\qquad\boxed{K_{\max}=6.00-4.50=1.50\,\mathrm{eV}}.$$

(b) Interpretation and further calculation

$$R\propto\mathcal I^3\quad\Rightarrow\quad\boxed{R(2\mathcal I)/R(\mathcal I)=8}.$$$$hf=2.00\,\mathrm{eV}<\phi\quad\Rightarrow\quad\text{the one-photon channel remains closed}.$$

Physical check

The intensity power law is a supplied perturbative model; at saturation or with competing channels it need not hold.