The intensity distribution of X-rays from two | vedclass

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(B) $1$. The minimum wavelength of the continuous $X$-ray spectrum is given by $\lambda_{\min} = \frac{hc}{eV}$.$2$. From the graph,we observe that $\

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$V_1 > V_2, Z_1 > Z_2$

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(B) $1$. The minimum wavelength of the continuous $X$-ray spectrum is given by $\lambda_{\min} = \frac{hc}{eV}$.$2$. From the graph,we observe that $\lambda_1  V_2$.$3$. The characteristic $K_{\alpha}$ line wavelength is determined by Moseley's law: $\sqrt{
u} = a(Z - b)$,which implies $
u \propto (Z - 1)^2$. Since $
u = \frac{c}{\lambda}$,we have $\lambda \propto \frac{1}{(Z - 1)^2}$.$4$. From the graph,the $K_{\alpha}$ peak for curve $1$ appears at a shorter wavelength than the $K_{\alpha}$ peak for curve $2$. Thus,$\lambda_{K\alpha, 1} $5$. This implies $(Z_1 - 1)^2 > (Z_2 - 1)^2$,which means $Z_1 > Z_2$.$6$. Combining these results,we get $V_1 > V_2$ and $Z_1 > Z_2$.

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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