Find the

(a) maximum frequency, and

(b) minimum wavelength of X-rays produced by 30 kV electrons.

(a) X-ray produced by the electron therefore has maximum photon energy (E_x) equal to energy (E) of the electron.

E = eV …(1)

Where magnitude of charge of the electron ‘e’ = 1.6 × 10^-19 C

Accelerating potential is V = 30 × 10³ V 3

Putting in equation (1) we get,

⇒ E = 1.6 × 10^-19 C × 30 × 10³ J

Also, E_x = hν

Where, E_x = maximum energy of the X-ray

And h = plank’s constant = 6.63 × 10^-34 J. sec

ν = max. frequency of X-ray

⇒ v_max = E_max/h

⇒

⇒ v_max= 7.24 × 10¹⁸ Hz

Max. frequency of X-ray is 7.24 × 10¹⁸ Hz

(b) Minimum wave length (λ) of X-ray is given by the following relation.

E_x = hν = hc/λ

∴ λ = hc / E_x

c = speed of light = 3 × 10⁸ m/s

⇒

⇒ λ = 0.041nm

Minimum wave length of X-ray is equal to 0.041nm