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(A) In an $X$-ray tube,the minimum wavelength $\lambda_{\min}$ is given by the Duane-Hunt law:$\lambda_{\min} = \frac{hc}{eV}$Taking the natural logar

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(A) In an $X$-ray tube,the minimum wavelength $\lambda_{\min}$ is given by the Duane-Hunt law:$\lambda_{\min} = \frac{hc}{eV}$Taking the natural logarithm on both sides:$\ln \lambda_{\min} = \ln \left(\frac{hc}{e}\right) - \ln V$This equation is of the form $y = mx + c$,where $y = \ln \lambda_{\min}$,$x = \ln V$,and the slope $m = -1$.Since the slope is $-1$ (which is negative),the graph of $\log \lambda_{\min}$ versus $\log V$ is a straight line with a negative slope. This corresponds to the graph shown in option $A$.

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