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Dual Nature of Radiation and Matter — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsDual Nature of Radiation and Matter5 Marks
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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