X-ray emitted from a copper target and a molybdenum target are found to contains a line of wavelength `22.85 n m` attributed to the `K_(alpha)` line of an impurity element . The `K_(alpha)` line of copper `(Z = 29)` and molybdenum `(Z = 42)` have wavelength `15.42 nm and 7.12 nm`, respectively. The atomic number of the impurity element is

Options

A. 22
B. 23
C. 24
D. 25

Answer

C

Explanation

Using Moseley's law, `V^(1//2) = a(z - b)`
`(( c)/(lambda_(1)))^(1//2) = a (z_(1) - b) and (( c)/(lambda_(1)))^(1//2) = a (z^(2) - b)`
`((lambda_(2))/(lambda_(1)))^((1)/(2)) = (a(z_(1) - b))/(a(z_(2) - b)) implies ((7.12)/(15.42))^((1)/(2)) = ((29 - b))/((42 - b))`
`(42 - b) = 1.47 (29 - b) implies = 1.44`
`((lambda_(1))/(lambda))^((1)/(2)) = ((z - 1.44))/((z_(1) - 1.44))`
`((15.42)/(22.85))^((1)/(2)) (27.56) = z - 1.44 implies = 24`