The Photoelectric Effect — Question 6

Question 6

A contact-voltage offset is inseparable from the intercept without calibration

A measured stopping voltage obeys $V_m=(hf-\phi)/e+V_c$. Independent calibration gives $V_c=+.150\,\mathrm V$. At wavelength 400 nm, $V_m=1.250\,\mathrm V$. 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 true stopping voltage and work function.

2. Find the apparent work function if the offset is ignored and explain why a frequency slope alone cannot detect this constant offset.

Question 6 - Solution

A contact-voltage offset is inseparable from the intercept without calibration

(a) Method and calculation

$$\boxed{V_s=V_m-V_c=1.100\,\mathrm V}.$$$$\boxed{\phi=hc/\lambda-eV_s=3.100-1.100=2.000\,\mathrm{eV}}.$$

(b) Interpretation and further calculation

$$\boxed{\phi_{\mathrm{apparent}}=3.100-1.250=1.850\,\mathrm{eV}}.$$$$\frac{dV_m}{df}=h/e,\qquad\text{intercept}=V_c-\phi/e.$$

Physical check

The calibrated sign of the offset matters. An uncalibrated intercept measures a combination of two quantities.