Characteristic X-rays of frequency `4.2xx10^18` Hz are produced when transitions from L-shell to K-shell take place in a certain target material. Use Mosley's law to determine the atomic number of the target material. Given Rydberg constant `R =1.1xx10^7 m^(-1)`.

Answer

`Z = 42`

Explanation

`DeltaE=hv=Rhc (Z-b)^(2) (1/n_(1)^(2)-1/n_(2)^(2))`
For K- series, `b=1 :. V=Rc (Z-1)^(2) (1/n_(1)^(2)-1/n_(2)^(2))`
substituting the values,
`4.2xx10^(18)=(1.1xx10^(7))(3xx10^(8))(Z-1)^(2)(1/1-1/4)`
`:. (Z-1)^(2)=1697implies Z-1 ~~41 implies Z=42`