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

Potential of the electrons, V = 30 kV = 3 x 10⁴ V

Hence, energy of the electrons, E = 3 x 10⁴ eV Where,

e = Charge on an electron = 1.6 x 10⁻¹⁹ C

Ans (a).
Maximum frequency produced by the X-rays = ν

The energy of the electrons is given by the relation: E = hν

Where, h = Planck’s constant = 6.626 x 10⁻³⁴ Js

Therefore ,  ν= 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.

Ans (b).

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

λ =c/ν = (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.