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?
Given:
Accelerating voltage, V = 50 KV
Energy of each electron is given by,
E = eV …(1)
Where,
e = Charge on electron = 1.6 × 10-19C
V = accelerating Voltage
Putting the values in equation (1)
E = 1.6 × 10-19C × 50 × 1000V
E = 8 × 10-15 J
De Broglie wave length is given by,
Where,
m = mass of electron
h = Planck’s constant = 6.6 × 10-19 Js
E = Energy
By putting the values in above equation we get,
λ = 5.4 × 10-12 m.
As compared to an optical telescope which uses yellow light, electron microscope has better resolving power (about 105 times better). As the resolving power is inversely proportional to the wavelength of light used.