Continuous X-rays are made to strike a tissue paper soaked with p… - Vidyadip

Question

Continuous X-rays are made to strike a tissue paper soaked with polluted water. The incoming X-rays excite the atoms of the sample by knocking out the electrons from the inner shells. Characteristic X-rays are analysed and the intensity is plotted against the wavelength. Assuming that only $\text{K}_\alpha$ intensities are detected, list the elements present in the sample from the plot. Use Moseley's equation v - (25 × 10¹⁴Hz)(Z - 1)².

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Answer

Given

v = (25 × 10¹⁴Hz) (Z -1)²

$\frac{\text{C}}{\lambda}=25\times10^{14}(\text{Z}-1)^2$

$\frac{\text{3}\times10^8}{78.9\times10^{-12}\times25\times10^{14}}=(\text{Z}-1)^2$

$(\text{Z}-1)^2=38.98$

$\text{Z}=39.98=40$ It is (Zr)

$\frac{3\times10^8}{146\times10^{-12}\times25\times10^{14}}=(\text{Z}-1)^2$

$(\text{Z}-1)^2=0.0008219\times10^6$

$\Rightarrow\text{Z}-1=28.669 $

$\text{Z}=29.669=30$ It is (Zn).

$\frac{3\times10^8}{158\times10^{-12}\times25\times10^{14}}=(\text{Z}-1)^2$

$(\text{Z}-1)^2=0.0007594\times10^6$

$\Rightarrow\text{Z}-1=27.5589$

$\text{Z}=28.5589=29$ It is (Cu).

$\frac{3\times10^8}{19\times10^{-12}\times25\times10^{14}}=(\text{Z}-1)^2$

$(\text{Z}-1)^2=0.000606\times10^6$

$\Rightarrow\text{Z}-1=24.6182 $

$\text{Z}=25.6182=26$ It is (Fe).

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