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Question 1

Find the
(a) maximum frequency, and
(b) minimum wavelength of X-rays produced by 30 kV electrons.

Answer

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 = ν

The energy of the electrons is given by the relation:

E =

Where,

h = Planck’s constant = 6.626 × 10−34 Js

So  v = E / h

      = 1.6 x 10-19 x 3 x 104 / 6.626 x 10-34 = 7.24 x 1018 Hz

Hence, the maximum frequency of X-rays produced is 7.24 x 1018 Hz

 

(b)The minimum wavelength produced by the X-rays is given as:

λ = c / v

= 3 x 108 / 7.24 x 1018 = 4.14 x 10-11 m = 0.0414 nm

Hence, the minimum wavelength of X-rays produced is 0.0414 nm.

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