# The Kα and Kβ X-rays of Molybdenum Have Wavelengths 0.71 a and 0.63 a Respectively. Find the Wavelength of Lα X-ray of Molybdenum. - Physics

Sum

The Kα and Kβ X-rays of molybdenum have wavelengths 0.71 A and 0.63 A respectively. Find the wavelength of Lα 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.)

#### Solution

Given:-
Wavelength of Kα X-rays of molybdenum,lambda_a = 0.71  "A"

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

Energy of KαX-rays (K_a)is given by

K_a = E_K - E_L      .....(1)

Energy of Kβ X-rays (K_β) is given by

K_β = E_K - E_L      .....(2)

Energy of La 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

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