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 K_α intensities are detected, list the elements present in the sample from the plot. Use Moseley's equation v − (25 × 10¹⁴Hz)(Z − 1)².

Answer 1

Given:
f = (25 × 10¹⁴ Hz) (Z − 1)^{2
$$\begin{gathered} \mathrm{or}\frac{c}{\lambda }=25\times {10}^{14}(\mathrm{Z}-1{)}^2 \\ (\mathrm{a})\frac{3\times {10}^8}{78.9\times {10}^{-12}\times 25\times {10}^{14}}=(\mathrm{Z}-1{)}^2 \\ \mathrm{or}(\mathrm{Z}-1{)}^2=.0.001520\times {10}^6=1520 \\ \Rightarrow \mathrm{Z}-1=38.98 \\ \mathrm{or}\mathrm{Z}=39.98=40 \\ \mathrm{Thus},\mathrm{it}\mathrm{is}(\mathrm{Zr}). \\ (\mathrm{b})\frac{3\times {10}^8}{146\times {10}^{-12}\times 25\times {10}^{14}}=(\mathrm{Z}-1{)}^2 \\ \mathrm{or}(\mathrm{Z}-1{)}^2=0.00082219\times {10}^6 \\ \mathrm{or}\mathrm{Z}-1=28.669 \\ \mathrm{or}\mathrm{Z}=29.669=30 \\ \mathrm{Thus},\mathrm{it}\mathrm{is}(\mathrm{Zn}). \\ (\mathrm{c})\frac{3\times {10}^8}{158\times {10}^{-12}\times 25\times {10}^4}=(Z-1{)}^2 \\ \mathrm{or}(\mathrm{Z}-1{)}^2=0.0007594\times {10}^4 \\ \mathrm{or}\mathrm{Z}-1=27.5559 \\ \mathrm{or}\mathrm{Z}=28.5589=29 \\ \mathrm{Thus},\mathrm{it}\mathrm{is}(\mathrm{Cu}). \\ (\mathrm{d})\frac{3\times {10}^8}{198\times {10}^{-12}\times 25\times {10}^4}=(\mathrm{Z}-1{)}^2 \\ \mathrm{or}(\mathrm{Z}-1{)}^2=0.000606\times {10}^4 \\ \mathrm{or}\mathrm{Z}-1=24.6162 \\ \mathrm{or}\mathrm{Z}=25.6162=26 \\ \mathrm{Thus},\mathrm{it}\mathrm{is}(\mathrm{Fe}). \end{gathered}$$}