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

Accroding of Moseley's law.
`sqrt(f)=a(Z-b)rArrsqrt(c/(lambda))=a(Z-b)`
For aluminium, `sqrt(c/(887))=a(13-b)" " ....(i)`
For copper, `sqrt((c)/(140))=a(29-b)" " ....(ii)`
On dividing, Eq. (ii) by Eq. (i) , we have,
`sqrt(887/(140))=(29-b)/(13-b)rArr2.5(13-b)=29-brArrb=2.3`
`:. sqrt(c/(140))=a(29-b)rArrsqrt((3xx10^(8))/(140xx10^(-12)))=a(29-2.3)`
`rArr1.46xx10^(9)=a(26-7)rArra=0.055xx10^(9)~~5xx10^(7)`
Now, for iron we can write as
`sqrt(c/(lambda))=(Z-b)=5xx10^(7)(26-2.3)=118.5xx10^(7)`
`rArr" " lambda=(3xx10^(8))/((118.5xx10^(7))^(2))=2.13xx10^(-10)=2Å`