Question

An electron is accelerated through 50 kV. What is the minimum wavelength photon it can produce when striking a target? *​

Answer 1

Given info : An electron is accelerated through 50 kV.

To find : the minimum wavelength when it can produce photon when striking a target.

solution : electron is accelerated through potential , V = 50kV

so, electric potential energy of electron, E = qV

= 50 × 10³ eV

= 50 × 10³ × 1.6 × 10^-19 J

= 8 × 10¯¹⁵ J

now electric potential energy = kinetic energy = P²/2m

where P is momentum and m is mass of electron.

so, 8 × 10¯¹⁵ = P²/(2 × 9.1 × 10¯³¹)

⇒8 × 2 × 9.1 × 10¯⁴⁶ = P²

⇒P = 12.066 × 10¯²³ Kgm/s

now using De-Broglie's wavelength equation,

λ = h/P = 6.63 × 10¯³⁴ Js/12.066 × 10¯²³ kgm/s

= 0.5494 × 10¯¹¹ m

= 5.494 × 10¯¹² m ≈ 5.5 pm

Therefore minimum wavelength would be 5.5 pm