Question

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

Answer 1

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.