Paper 4 Quantum Physics Answers

Q1 Determination of the Planck Constant

1. Axes correctly oriented and labelled [1]; sensible scales [1]; six points accurately plotted [2]; best-fit straight line [1].

2. Gradient $\approx 0.413\mathrm{V}$ per $10^{14}\mathrm{Hz}=4.13\times 10^{-15}\mathrm{V}\mathrm{H}{\mathrm{z}}^{-1}$. Accept graph-consistent values. [2]

3. Since the gradient is $h/e$,

   $$h=e(4.13\times 10^{-15})\approx 6.61\times 10^{-34}\mathrm{J}\mathrm{s}.$$

   [2]

4. The intercept is approximately $f_0=4.84\times 10^{14}\mathrm{Hz}$. At threshold, $\Phi =h{f}_0$, so $\Phi /e\approx 2.00\mathrm{eV}$. Accept graph-consistent values. [2]

5. Any two: uncertainty in identifying zero photocurrent; contact-potential variation; imperfectly monochromatic light; frequency calibration; surface contamination or changing work function; low-current electrical noise. [2]

Q2 X-ray Spectrum Investigation

1. Higher accelerating voltage gives larger maximum photon energy, so ${\lambda }_{min}=hc/eV$ decreases. [2]
2. Characteristic peaks shift because electron energy-level spacings are different in different target atoms. [2]
3. Use shielding, interlocks, distance, short exposure times, or do not operate with exposed beam. [1]