Calculate the wavelength of the emitted characteristic X-ray from a tungsten `(Z = 74)` target when an electrons drops from an `M` shell to a vacancy in the shell.

Explanation

Tungsten is a multielectron atom. Due to the shielding of the nuclear charge by the negative charge of the inner core electrons, each electron is subject to an effective nuclear charge `Z_(eff)` which is different for different shells.
For an electron in the `K shell , sigma = 1`.
Thus, `Z_(eff) = Z - sigma = Z - 1`
Here, as electron drops from `M shell (n = 3) to K shell (n = 1)`, we call the radiated emission `K_(beta)` X-ray and from is given as
`(1)/(lambda_(k_beta)) = R (Z- 1)^(2) [1/1^(2)-1/3^(2)]
or `
or `(1)/(lambda_(k beta)) = 10967800 xx (74- 1)^(2) [(8)/(9)]`
or `lambda_(k beta) = 0.192 Å`