Electron microscopes (A-level only) Flashcards – AQA A-level Physics (7408)

What kinetic energy and momentum relation applies to a non-relativistic electron accelerated through voltage $V$ from negligible initial kinetic energy?

$K=eV=\frac{p^2}{2m_e}$

How is an electron’s de Broglie wavelength related to its momentum?

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

What equation relates an electron’s wavelength to its accelerating voltage, in both forms? Assume negligible initial kinetic energy and non-relativistic motion.

$\lambda=\frac{h}{\sqrt{2m_e eV}}, \qquad V=\frac{h^2}{2m_e e\lambda^2}$

Approximately what accelerating voltage gives an electron a wavelength of $10^{-10}\,\mathrm{m}$?

About $150\,\mathrm{V}$, or order $10^2\,\mathrm{V}$.

How does increasing the accelerating voltage affect an electron’s momentum and wavelength?

Its momentum increases and its wavelength decreases.

What does a scanning tunnelling microscope (STM) use to scan a conducting surface?

A sharp conducting tip held very close to the surface.

How is a current produced across the gap in an STM?

A potential difference allows electrons to tunnel across the gap, rather than cross it by a classical path.

How does the tunnelling current in an STM depend on the tip–surface separation?

It changes strongly with the separation.

What does an STM feedback system adjust during a scan, and what does it keep constant?

It adjusts the tip height to keep the tunnelling current constant.

How does an STM build an image, and what resolution can it achieve?

It uses changes in tip height to build a surface image with atomic-scale resolution.