Question

The wavelength $\lambda$ of $K_{\beta }$ X-Ray is given by:

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$K_{\beta }$ characteristic X-Ray phton is emitted when an electron from the M shell jumps to fill the electronic vacancy created in K shell.
Now, if we refer to the Energy Level Diagram, we find that The atomic energy when there is a vacancy in K shell is $E_K$.
Also the atomic energy when the vacancy gets created in M shell is $E_M$.
We see that $E_M$ < $E_K$.
So the atom has lost this energy. How much ?
$E_K-E_M$
This energy appears as the energy of $K_{\beta }$ characteristic X-Ray phton.
Hence $\frac{hc}{{\lambda }_{K\beta }}=E_K-E_M.$
Which gives,
$\frac{1}{{\lambda }_{K\beta }}=E_K-E_M.$