If the wavelength of the emitted characterstics `X`-ray from a silver `(Z=47)` target when electron drops from `M`-shell to a vacancy in the `L`-shell is `1.4k A^(@)`. Then find the value of `k`. [Screening constant for `L_(alpha)=7.4`.]

Explanation

Because of the shielding of the nuclear charge by the negative charge of the inner core electrons the energy of an electron in `n^(th)` level of a multi-electron atom is given by
`E_(n)=-(13.6)/(n^(2))Z_(eff)^(2)eV`
For `L_(alpha)` line an electron drops from `M` shell to `L` shell
`(1)/(lambda)=R(Z-7.4)^(2)((1)/(2^(2))-(1)/(3^(2)))=R(Z-7.4)^(2)((5)/(36))`
`(1)/(lambda)=109737xx(47-7.4)^(2)xx(5)/(36)cm^(-1)`
`lambda=(1)/(2.39xx10^(7))cm^(-1)=(10^(8))/(2.39xx10^(7))=4.2A^(@)`