Thursday, February 24, 2011

Mastering Physics: ± Resolution of an Electron Microscope

An electron microscope is using a 1.00-keV electron beam. An atom has a diameter of about 10^{-10} meters.

Part A
What is the wavelength lambda of electrons in this microscope?
Express your answer in nanometers to three significant figures.

  lambda  = 3.88×10−2
  {\rm nm}
Compare this wavelength to the typical size of an atom.

Part B
Can an individual atom theoretically be resolved using this electron microscope?


Note that in practice a resolution better than \sim 0.5 \:{\rm nm} cannot be achieved with an electron microscope. This is due, in part, to the fact that the focal length of a magnetic lens depends on the electron speed, which is never the same for all electrons in the beam.
Part C
Suppose we replace the electron beam with a proton beam. What proton energy is needed to achieve the same resolution as the electron beam in Part A?
Express your answer in electron volts to three significant digits.

  {\rm eV}
In principle, we could use proton beams with relatively low energy to get great resolution. However, in practice, it is much easier to create an electron beam than it is to create a proton beam, which is why electron microscopes have become the norm.

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