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NCERT Class XII Chapter
Dual Nature of Radiation and Matter
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Question : 31
Total: 37
Crystal diffraction experiments can be perfor-med using X-rays, or electrons accelerated through appropriate voltage. Which probe has greater energy? An X-ray photon or the electron? (For quantitative comparison, take the wavelength of the probe equal to 1 Å, which is of the order of interatomic spacing in the lattice) (me = 9.11 × 10–31 kg).
Solution:  
Order of interatomic spacing is 1 Å in the crystal lattice. So, for diffraction to take place the wavelength should be of the same order.
For X-ray photon (energy for wavelength of 1 Å)
E =
hc
λ
 =
6.63×10−34×3×108
10−10×1.6×10−19
 eV = 12.4 × 103 eV = 12.4 KeV
For electron (energy to provide wavelengthof 1 Å)
momentum required P =
h
λ
 =
6.63×10−34
10−10
 = 6.63 × 10−24kgms−1
Kinetic energy K =
p2
2m
 =
(6.63×10−24)2
2×9.11×10−31
 J
K =
(6.63×10−24)2
2×9.11×10−31×1.6×10−19
 eV = 150. eV
Thus in order to produce same wavelength X-ray photon should have higher energy than electron.
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