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Wave Optics

Question
CBSEENPH12038470

(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

We are given an x-ray tube.

Wavelength of the radiation, λ = 0.45 Å = 0.45 x 10–10 m
Planck's constant, h = 6.62 x 10–34 Js
speed of light, c = 3 x 108 ms–1 

(a) The maximum energy of photon is given by, 
                E = hv = hcλ 

            E = 6.62 × 10-34 × 3 × 1080.45 × 10-10   = 44 × 10-16J                               
 i.e.,         E = 44 × 10-161.6 × 10-19eV    = 27.5 × 103 eV   = 27.5 keV. 

(b) To produce electrons of 27.5 keV, accelerating potential of 27.5 kV to 30 KV is required.

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