Homework 1 for the electron microscopy class
The wavelength of photons is given by the expression =hc/E = 12396 eV- /E where h is
Planck’s constant and c is the speed of light (in the medium). For electrons, the equivalent
expression is  = h/p where p is the electron momentum: p = mv. In classical mechanics the
energy of a particle is given by E = ½ mv2 where m is its mass and v is its velocity.
1. The wavelength of visible light typically falls within the range of 400 - 800 nm. What energy
range does this correspond to?
2. Electrons in electron microscopes are typically accelerated by potentials of 100 V - 30 kV.
(a) To what energies are they accelerated?
(b) Calculate the corresponding wavelengths.
3. The resolution of a microscope is approximately equal to the wavelength of the light being
used to view images. What is the approximate resolution of (a) an optical microscope using
visible light and an electron microscope operating at (b) 100 V and (c) 30 kV, assuming the
resolution to be diffraction limited in all cases.
4. Particles are generally considered to be relativistic if their velocity is greater than 0.1c. Are
relativistic effects important for any of the electrons in our scanning electron microscopes?
Extra credit: How would relativistic effects, if present, manifest themselves?
5. Conveniently, the door opening in the chamber of the Leo is 10” square. (a) Calculate the net
force on the door when the chamber pressure is 1 Torr; (b) Calculate the net force on the door
when the chamber pressure is 10-6 Torr; (c) Are your answers impacted by the fact that the
microscope is located in Salt Lake City? (d) If so, what is the magnitude of this correction? If
not, why not?
Read Goldstein chapter 1 to the italic section above 1.33; study the remainder of chapter 1 and
sections 2.1 – 2.2.3.
All due Friday 5 September.

Homework for the electron microscopy class