if the frequency fo `K_a` X-ray emitted from the element with atomic number 31 is f, then the frequency of `K_a` x-ray emitted from the elemet with atomic number 51 would be

Options

A. `(5f)/(3)`
B. `(51f)/(31)`
C. `(9f)/(25)`
D. `(25f)/(9)`

Answer

D

Explanation

`sqrtf prop (Z-1) for K-series
`:. fprop (Z-1)^2`
`(f_2)/(f_1) = ((Z_2 - 1))^2/((Z_1 - 1))^2`
`:. F_2 =((Z_2 -1)/(Z_1 -1))^2 f_1`
`=((51 -1)/(31-1))^2 f`
`=(25)/(9) f`.