The wavelength of `k_alpha` line in the X-ray spectrum for tungsten (Z=74) is 200 Å. What would be the wavelength of same line for platinum Z =78 ?

Explanation

According to Moseley's law
`sqrtf=a(Z-b)`
`therefore f=a^2(Z-b)^2`
for `k_alpha` line in X-ray spectrum `a="3Rc"/4` [R is Rydberg constant & c is speed of light ] and b=1
So `f=c/lambda=a^2(Z-b)^2`
`rArr c/lambda_1=a^2(74-1)^2`....(1)
and `c/lambda_2=a^2(78-1)^2` ....(2)
Dividing (1) and (2) we get `lambda_2=lambda_1(73/77)^2`
`rArr lambda_2=200xx(73/77)^2`
`rArr lambda_2=179.76 Å`