The wavelength of the chartacristic Ka X - rays of iron and potassium are `1.931 xx 10^(-8) and 3.737 xx 10^(-8)` respectively .What is the atomic number of an element for which the characteristic Ka wavelength is `2.289 xx 10^(-8) cm` ?

Explanation

From moseley's law , we get
`sqrt(v) prop Z`
or `v = aZ^(2)`
`or (c )/(lambda) = aZ^(2) (v = (C )/(lambda))`
or ` lambda = (c )/(aZ^(2))`
or `lambda prop (1)/(Z^(2))`
For fe, `lambda_(1) prop (1)/((26)^(2))`
For K, `lambda_(2) prop (1)/((19)^(2))`
For X,` lambda_(3) prop (1)/((Z)^(2))`
Now `(lambda_(1))/(lambda_(3)) = ((Z)^(2))/(26)^(2)`
or `(Z^(2)) = (lambda_(1))/(lambda_(3)) xx (26)^(2)`
or `(Z^(2)) = (1.931 xx 10^(-8))/(2.289 xx 10^(-8)) xx (26)^(2)`
or `Z = 23.88 = 24`
Again `(lambda_(2))/(lambda_(3)) = (Z)^(2)/((19)^(2))`
or `(Z^(2)) = (lambda_(2))/(lambda_(3)) xx (19)^(2)`
or `Z^(2) = (3.737 xx 10^(-8))/(2.289 xx 10^(-8)) `
or `Z = 24.27 = 24`