The `k_alpha` X-rays of aluminium (Z = 13 ) and zinc ( Z = 30) have wavelengths 887 pm and 146 pm respectively. Use Moseley\'s law `sqrt v = a(Z - b)` to find the wavelength of the `K_alpha` X-ray of iron (Z = 26).

Explanation

`sqrt(v)=a(Z-b)` implies `sqrt(c/lambda)=a(Z-b)`
Aluminium: `sqrt(c/887)=a(13-b) ...(i)`
Zinc: `sqrt(c/146)=a(30-b) ...(ii)`
(ii)/(i)
`sqrt(887/146)=(30-b)/(13-b) implies 2.5(13-b)=30-b`
`b=1.4`
`sqrt(c/146)=a(30-b)`
`sqrt((3xx10^(8))/(146xx10^(-12))) =a(30-1.4)`
`1.43xx10^(8)=a(28.6) implies a=5xx10^(7) (Hz)^(1//2)`
Iron: `sqrt(c/lambda)=a(Z-b)=5xx10^(7)(26-1.4)=123xx10^(7)`
`lambda=(3xx10^(8))/((123xx10^(7))^(2))=1.98xx10^(-10) m`
`=198 p m`