The Photoelectric Effect — Question 2

Question 2

The slope of stopping potential measures Planck’s constant independently of the intercept

An ideal photoelectric experiment gives $(f_1,V_1)=(6.00\times10^{14}\,\mathrm{Hz},.484\,\mathrm V)$ and $(f_2,V_2)=(9.00\times10^{14}\,\mathrm{Hz},1.726\,\mathrm V)$. Contact offsets are absent. Take $e=1.60\times10^{-19}\,\mathrm C$.

1. Infer $h/e$ and h from the slope.

2. Find the work function and threshold frequency.

Question 2 - Solution

The slope of stopping potential measures Planck’s constant independently of the intercept

(a) Method and calculation

$$V_s=(h/e)f-\phi/e,\quad\boxed{h/e=\frac{1.726-.484}{3.00\times10^{14}}=4.14\times10^{-15}\,\mathrm{V\,s}}.$$$$\boxed{h=6.624\times10^{-34}\,\mathrm{J\,s}}.$$

(b) Interpretation and further calculation

$$\phi/e=(h/e)f_1-V_1=2.484-.484=\boxed{2.00\,\mathrm V}.$$$$\boxed{\phi=2.00\,\mathrm{eV}},\quad\boxed{f_0=\phi/h=4.83092\times10^{14}\,\mathrm{Hz}}.$$

Physical check

The slope uses differences and removes the work-function intercept. The inferred h reflects the stated rounded data.