E.2 Quantum physics (HL)：練習問題

Which of the following best describes a photon?

A graph is plotted showing the variation of the maximum kinetic energy \(E_{max}\) of photoelectrons with the frequency \(f\) of incident radiation. What does the x-intercept of this graph represent?

Quantum tunnelling allows a particle to pass through a potential barrier even when its kinetic energy is less than the potential energy of the barrier. Which of the following changes would increase the probability of a particle tunnelling through a barrier?

The uncertainty in the position of an electron is \(5.0 \times 10^{-10}\text{ m}\). What is the minimum uncertainty in the momentum of the electron?
(Use \(\Delta x \Delta p \ge \frac{h}{4\pi}\) and \(h = 6.63 \times 10^{-34}\text{ J s}\))

In the Schrödinger model of the atom, the wavefunction \(\psi\) describes the state of an electron. What is the physical significance of the quantity \(|\psi|^2 \Delta V\) at a specific point in space?

The Heisenberg Uncertainty Principle sets fundamental limits on measurement.
(a) State the principle in terms of position (\(\Delta x\)) and momentum (\(\Delta p\)).
(b) An electron is confined within a nucleus of diameter \(1.0 \times 10^{-14}\text{ m}\). Estimate the minimum uncertainty in its momentum.
(c) Use your result from part (b) to explain why electrons are not expected to exist within the nucleus, considering their relativistic energy levels.

Wave-particle duality is a central concept in quantum mechanics.
(a) Explain how the electron diffraction experiment provides evidence for the wave nature of matter.
(b) Calculate the de Broglie wavelength of an alpha particle (mass \(6.64 \times 10^{-27}\text{ kg}\)) moving at a speed of \(1.5 \times 10^7\text{ m s}^{-1}\).
(c) If the position of this alpha particle is measured with an uncertainty of \(1.0 \times 10^{-12}\text{ m}\), determine the minimum uncertainty in its velocity.