The K_ X-rays from certain elements are given below. Draw a Mosel… - Vidyadip

Question

The $\text{K}_\beta\ X-$rays from certain elements are given below. Draw a Moseley-type plot of $\sqrt{\text{v}}$ versus $Z$ for $\text{K}_\beta$ radiation.

Element	$Ne$	$P$	$Ca$	$Mn$	$Zn$	$Br$
Energy $(keV)$	$0.858$	$2.14$	$4.02$	$6.51$	$9.57$	$13.3$

✓

Answer

$\text{K}_\text{B}$ radiation is when the e jumps from
$n = 3$ to $n = 1 ($here $n$ is principal quantum no$)$
$\Delta\text{E}=\text{hv}=\text{Rhc(z-h)}^2\Big(\frac{1}{2^2}-\frac{1}{3^2}\Big)$
$\sqrt{\text{v}}=\sqrt{\frac{9\text{RC}}{8}}(\text{z}-\text{h})$
$\therefore\sqrt{\text{v}}\propto\text{z}$
Second method :
We can directly get value of $v\ b$
$hv =$ Energy
$\Rightarrow\text{v}=\frac{\text{Energy(in Kev)}}{\text{h}}$
This we have to find out $\sqrt{\text{v}}$ and draw the same graph as above.

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