\[{{V}_{1}}\]and\[{{V}_{2}}\]and using different target materials of atomic numbers\[{{Z}_{1}}\]and\[{{Z}_{2}}\]is shown in the figure. Which of the following inequalities is true?
A) \[{{V}_{1}}>{{V}_{2}}\]and \[{{Z}_{1}}<{{Z}_{2}}\]
B) \[{{V}_{1}}>{{V}_{2}}\]and \[{{Z}_{1}}>{{Z}_{2}}\]
C) \[{{V}_{1}}<{{V}_{2}}\]and\[{{Z}_{1}}>{{Z}_{2}}\]
D) \[{{V}_{1}}={{V}_{2}}\]and\[{{Z}_{1}}<{{Z}_{2}}\]
Correct Answer: A
Solution :
\[{{\lambda }_{\min }}=\frac{hc}{eV}\] \[\Rightarrow \] \[\lambda \propto \frac{1}{V}\] \[(\because {{\lambda }_{2}}>{{\lambda }_{1}})\] \[\Rightarrow \] \[{{V}_{1}}>{{V}_{2}}\] From Moseley's law\[\sqrt{v}=a(Z-b)\] \[v\propto {{(Z-1)}^{2}}\] \[\Rightarrow \] \[\lambda \propto \frac{1}{{{(Z-1)}^{2}}}\] \[\left[ \because v\propto \frac{1}{\lambda } \right]\] According to diagram\[{{\lambda }_{1}}>{{\lambda }_{2}}\] \[\Rightarrow \] \[{{Z}_{2}}>{{Z}_{1}}\]
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