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Question
Find the (a) maximum frequency and (b) minimum wavelength of X-rays produced by 30 kV electrons.
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Solution
Potential of the electrons, V = 30 kV = 3 × 104 V
Hence, energy of the electrons, E = 3 × 104 eV
Where,
e = Charge on an electron = 1.6 × 10−19 C
(a) Maximum frequency produced by the X-rays = v
The energy of the electrons is given by the relation.
E = hv
Where,
h = Planck’s constant = 6.626 × 10−34 Js
∴ v = `E/h`
= `(1.6 xx 10^(-19) xx 3 xx 10^4)/(6.626 xx 10^(-34))`
= 7.24 × 1018 Hz
Hence, the maximum frequency of X-rays produced is 7.24 × 1018 Hz.
(b) The minimum wavelength produced by the X-rays is given as:
`lambda = c/v`
= `(3 xx 10^8)/(7.24 xx 10^18)`
= 4.14 × 10−11 m
= 0.0414 nm
Hence, the minimum wavelength of X-rays produced is 0.0414 nm.
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