Question

The wavelengths of K_α and L_α X-rays of a material are 21.3 pm and 141 pm respectively. Find the wavelength of K_β X-ray of the material.

(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 K_α X-ray, `lambda_1 = 21.3  "pm"`

Wavelength of L_α X-ray, `lambda_2 = 141  "pm"`

Energy of K_α X-ray (`E_1`) is given by

`E_1 = 1242/(21.3 xx 10^-3)`

= `58.309 xx 10^3  "eV"`

Energy of L_α X-ray (`E_2`) is given by 

`E_2 = 1242/(141 xx 10^-5)`

= `8.8085 xx 10^3  "eV"`

Energy of K_β X-ray (`E_3`) will be

`E_3 = E_1 + E_2`

`E_3 = (58.309 + 8.809) xx 10^3  "eV"`

`E_3 = 67.118 xx 10^3  "eV"`

Wavelength of K_β X-ray (`lambda`) is given by

`lambda = (hc)/(E_3) = 1242/(67.118 xx 10^3)`

= `18.5 xx 10^-3  "nm" = 18.5  "pm"`