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NCERT Class XII Chapter
Dual Nature of Radiation and Matter
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Question : 31 of 37
Marks: +1, -0
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 × 10−3110^{-31} kg).
Solution:  
Order of interatomic spacing is 1 Ã… 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 Ã…)
E = hcλ\frac{hc}{\lambda} = 6.63×10−34×3×10810−10×1.6×10−19\frac{6.63\times10^{-34}\times3\times10^8}{10^{-10}\times1.6\times10^{-19}} eV = 12.4 × 10310^3 eV = 12.4 KeV
For electron (energy to provide wavelengthof 1 Ã…)
momentum required P = hλ\frac{h}{\lambda} = 6.63×10−3410−10\frac{6.63\times10^{-34}}{10^{-10}} = 6.63 × 10−24 kgms−110^{-24}\ \mathrm{kgms}^{-1}
Kinetic energy K = p22m\frac{p^2}{2m} = (6.63×10−24)22×9.11×10−31\frac{(6.63\times10^{-24})^2}{2\times9.11\times10^{-31}} J
K = (6.63×10−24)22×9.11×10−31×1.6×10−19\frac{(6.63\times10^{-24})^2}{2\times9.11\times10^{-31}\times1.6\times10^{-19}} eV = 150. eV
Thus in order to produce same wavelength X-ray photon should have higher energy than electron.
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