Question

The wavelength of K_α X-ray of tungsten is 21.3 pm. It takes 11.3 keV to knock out an electron from the L shell of a tungsten atom. What should be the minimum accelerating voltage across an X-ray tube having tungsten target which allows production of K_α X-ray?

(Use Planck constant h = 6.63 × 10^-34 Js= 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

Answer 1

Given:-

Wavelength of X-ray of tungsten,

`lambda` = 21.3 pm

Energy required to take out electron from the L shell of a tungsten atom, E_L = 11.3 keV

Voltage required to take out electron from the L shell of a tungsten atom, V_L = 11.3 kV

Let E_K and E_L be the energies of K and L, respectively.

`E_K - E_L = (hc)/lambda`

Here,

h = Planck's constant

c = Speed of light

`E_K - E_L = (1242  "eV" - "nm")/(21.3 xx 10^-12)`

`E_K - E_L = (1242 xx 10^-9  "eV")/(21.3 xx 10^-12)`

`E_K - E_L = 58.309  "keV"`

`E_L = 11.3  "keV"`

`therefore E_K  = 69.609  "keV"`

Thus, the accelerating voltage across an X-ray tube that allows the production of K_α X-ray is given by

V_K = 69.609 kV