Question

The K_α and K_β X-rays of molybdenum have wavelengths 0.71 A and 0.63 A respectively. Find the wavelength of L_α X-ray of molybdenum.

(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-rays of molybdenum,`lambda_a = 0.71  "A"`

Wavelength of K_β X-rays of molybdenum,`lambda_b = 0.63  "A"`

Energy of K_αX-rays (`K_a`)is given by

`K_a = E_K - E_L`      .....(1)

Energy of K_β X-rays (`K_β`) is given by

`K_β = E_K - E_L`      .....(2)

Energy of L_a X-ray (`L_a`) is given by 

`K_L = E_L - E_M`

Subtracting (2) from (1),

`K_α - K_β = E_M - E_L = -K_L`

or  `K_L = K_β - K_α`

`K_L = (3 xx 10^8)/(0.63 xx 10^-10) - (3 xx 10^8)/(0.71 xx 10^-10)`

`K_L = 4.761 xx 10^-18 - 4.225 xx 10^18`

`K_L = 0.536 xx 10^18  "Hz"`

Again , `lambda = (3 xx 10^8)/(0.536 xx 10^-18)`

⇒ `lambda = 5.6 xx 10^-10 = 5.6  Å`