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Q.

The intensity distribution of X-rays from two Coolidge tubes operated on different voltages $V_{1} and V_{2}$ and using
different target materials of atomic numbers $Z_{1} and Z_{2}$ is shown in the figure. Which one of the following inequalities is true?

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a

$V_{1} > V_{2}; Z_{1} < Z_{2}$

b

$V_{1} > V_{2}; Z_{1} > Z_{2}$

c

$V_{1} < V_{2}; Z_{1} > Z_{2}$

d

$V_{1} = V_{2}; Z_{1} < Z_{2}$

answer is A.

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Detailed Solution

By Moseley'slaw,

$\begin{array}{l} l_{\min} = \frac{hc}{eV} \Rightarrow λ \propto \frac{1}{V} \\ ∴ λ_{2} > λ_{1} (see graph) \Rightarrow V_{1} > V_{2} \\ \sqrt{v} = a (Z - b) . . . (Moseley' s law) \\ v \propto {(Z - 1)}^{2} \Rightarrow λ \propto \frac{1}{{(Z - 1)}^{2}} . (∴ v \propto \frac{1}{λ}) \\ λ_{1} > λ_{2} (see graph for characteristic lines) \Rightarrow Z_{2} > Z_{1} . \end{array}$

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