Paper 3 Quantum Physics Drills

Q1 Photoelectrons and Uncertainty

Ultraviolet radiation of wavelength $360\mathrm{nm}$ illuminates a metal of work function $2.10\mathrm{eV}$. Use $h=6.63\times 10^{-34}\mathrm{J}\mathrm{s}$, $c=3.00\times 10^8\mathrm{m}{\mathrm{s}}^{-1}$, $e=1.60\times 10^{-19}\mathrm{C}$ and $m_e=9.11\times 10^{-31}\mathrm{kg}$.

1. Calculate the photon energy in eV. [2]
2. Hence calculate the maximum kinetic energy and stopping potential of the emitted electrons. [3]
3. Show that the maximum electron momentum is approximately $6.3\times 10^{-25}\mathrm{kg}\mathrm{m}{\mathrm{s}}^{-1}$. [3]
4. The uncertainty in an electron’s momentum is $5.0\%$ of this value. Using $\Delta p\Delta x\gtrsim h$, estimate the minimum uncertainty in its position. [2]
5. Explain why increasing the radiation intensity at the same wavelength does not reduce this minimum position uncertainty for electrons emitted with the stated momentum uncertainty. [2]

Q2 Uncertainty Principle

1. Explain qualitatively why a particle localised in a small region has a larger momentum uncertainty. [3]
2. State one physical situation where wave-packet thinking is more appropriate than a single infinite sinusoidal wave. [1]
3. Explain why the uncertainty principle is not mainly a limitation of poor instruments. [2]