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.

Answer 1

Given :
Wavelength of K_α X-rays,  `lambda_1`= 0.71 A
Wavelength of K_β X-rays, `lambda_2` = 0.63 A

For L_a X-ray of molybdenum,
 a = 57
 b = 1
From Moseley's equation,

`sqrt(v) = a(Z - b)`

Here, v = frequency of X-ray
         Z = atomic number of the element

`sqrt(v) = a(Z - b)`

⇒ `sqrt(v) = a(57 - 1)`

= `a xx 56`       ...(1)

For `Cu` (29),

`sqrt(1.88 xx 10^18) = a(29 - 1) = 28 a        ...(2)`

Dividing (1) and (2)

`sqrt(v/(1.88 xx 10^18)) = (a xx 56)/(a xx 28) = 2`

⇒ `v = 1.88 xx 10^18 xx (2)^2`

= `4 xx 1.88 xx 10^18`

= `7.52 xx 10^18  "Hz"`