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(D) According to Wien's displacement law,$\lambda_m T = b$,where $b$ is Wien's constant.If $v_m$ is the frequency corresponding to the wavelength $\la

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$B$

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(D) According to Wien's displacement law,$\lambda_m T = b$,where $b$ is Wien's constant.If $v_m$ is the frequency corresponding to the wavelength $\lambda_m$,then $\lambda_m = \frac{c}{v_m}$.Substituting this into the displacement law,we get $\left(\frac{c}{v_m}\right) T = b$.Rearranging the terms,we find $v_m = \left(\frac{c}{b}\right) T$.Since $c$ (speed of light) and $b$ (Wien's constant) are constants,$v_m \propto T$.This represents a linear relationship passing through the origin,which corresponds to the straight line labeled $B$ in the graph.Therefore,option $D$ is the correct answer.

For a perfectly black body,a graph is plotted between the frequency of radiation with maximum intensity $(v_m)$ and the absolute temperature $T$. Which of the following graphs is correct?

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