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NCERT Class XII Chapter
Dual Nature of Radiation and Matter
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Question : 33
Total: 37
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:  
K.E. of an electron, accelerated by voltage of 50 kV.
K = 50 keV = 1.6 × 10–19 × 5 × 104 J = 8 × 10–15 J
∴ de Broglie wavelength associated with electron
λ =
h
√2mK
 =
6.63×10−34
√2×9.11×10−31×8×10−15
λ =
6.63×10−11
12.07
 m = 5.5 × 10−12 m
Wavelength of yellow light, λy = 5.9 × 10–7 m.
Resolving power of a microscope α
1
λ
∴
Resolving‌power‌of‌electron‌microscope
Resolving‌power‌of‌optical‌microscope
=
λy
λ
 =
5.9×10−7
5.5×10−12
 = 105
Thus, the resolving power of an electron microscope is about 105 times greater than that of an optical microscope.
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