Question
An electron microscope uses electrons accelerated by a voltage of 50 kV. Determine the de-Broglie wavelength associated with the electrons. If other factors (such as numerical aperture, etc.) are taken to be roughly the same, how does the resolving power of an electron microscope compare with that of an optical microscope which uses yellow light?
Solution
Given,
Accelerating voltage, V = 50 kV
∴ Energy of electrons, E = eV = 50 keV
or, Energy, E = 50 x 103 x 1.6 x 10–19 J
De-broglie wavelength is given by,
Resolving power of microscope
where, .
Resolving power of a microscope is inversely proportional to the wavelength of the radiation used.
Since the wavelength of yellow light is 5.99 x 10–7 m, so it follows that electron microscope will have resolving power 105 times that of optical microscope.
Accelerating voltage, V = 50 kV
∴ Energy of electrons, E = eV = 50 keV
or, Energy, E = 50 x 103 x 1.6 x 10–19 J
De-broglie wavelength is given by,
Resolving power of microscope
where, .
Resolving power of a microscope is inversely proportional to the wavelength of the radiation used.
Since the wavelength of yellow light is 5.99 x 10–7 m, so it follows that electron microscope will have resolving power 105 times that of optical microscope.
