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NCERT Class XII Chapter
Dual Nature of Radiation and Matter
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Question : 23 of 37
Marks: +1, -0
(a) An X-ray tube produces a continuous spectrum of radiation with its short wavelength end at 0.45 Å. What is the maximum energy of a photon in the radiation?
(b) From your answer to (a), guess what order of accelerating voltage (for electrons) is required in such a tube ?
Solution:  
(a) Minimum wavelength corresponds to maximum energy photons.
EmaxE_{\text{max}} = hcλmin\frac{hc}{\lambda_{\text{min}}} = 6.3×10−34×3×1080.45×10−10\frac{6.3 \times 10^{-34} \times 3 \times 10^8}{0.45 \times 10^{-10}} J
or EmaxE_{\text{max}} = .63×10−34×3×1080.45×10−10×1.×10−19\frac{.63 \times 10^{-34} \times 3 \times 10^8}{0.45 \times 10^{-10} \times 1. \times 10^{-19}} eV = 27. × 10310^{3} eV = 27.6 eV
(b) In order to emit photons from the surface of energy 27.6 keV, the incident electrons striking on surface should have higher energy i.e., of the order of 30 keV.
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