Wave–particle duality (A-level only) Flashcards – AQA A-level Physics (7408)

What is the de Broglie wavelength of a particle with momentum $p$, in terms of the Planck constant $h$?

$\lambda = \frac{h}{p}$

How much kinetic energy does an electron gain when accelerated from rest through a potential difference $V$?

$E_k = eV$, where $e$ is the magnitude of the electron charge.

What is the non-relativistic relationship between kinetic energy and momentum for a particle of mass $m$?

$E_k = \frac{p^2}{2m}$

What is the non-relativistic momentum of an electron accelerated from rest through a potential difference $V$?

$p = \sqrt{2meV}$, where $m$ is the electron mass and $e$ is the magnitude of its charge.

What is the non-relativistic de Broglie wavelength of an electron accelerated from rest through a potential difference $V$?

$\lambda = \frac{h}{\sqrt{2meV}}$, where $m$ is the electron mass, $e$ is the magnitude of its charge, and $h$ is the Planck constant.

Why can a crystal diffract a beam of low-energy electrons?

The electrons’ de Broglie wavelength is comparable to the spacing of atoms in the crystal.

What does the intensity pattern from electron diffraction provide evidence for?

Electrons exhibit wave behaviour.

How does increasing electron speed affect momentum and de Broglie wavelength?

Momentum increases, so the de Broglie wavelength decreases.

For the same crystal, how does changing electron speed affect the diffraction pattern?

Increasing speed gives smaller diffraction angles, so the pattern contracts. Decreasing speed gives larger angles, so it spreads out.