For a perfectly black body, the graph is plotted between the frequency of radiation with maximum intensity…
For a perfectly black body, the graph is plotted between the frequency of radiation with maximum intensity $\left(v_{\mathrm{m}}\right)$ and the absolute temperature ' $\mathrm{T}$ '. Out of the following which is the correct graph?
C
A
D
B
Solution
According to Wein's displacement law $\lambda_{\mathrm{m}} \mathrm{T}=\mathrm{b}=$ Wein constant
If $v_m$ is the frequency corresponding to wavelength $\lambda_m$, then
$\left(\frac{\mathrm{c}}{\mathrm{u}_{\mathrm{m}}}\right) \mathrm{T}=\mathrm{b}$
or $\mathrm{u}_{\mathrm{m}}=\frac{\mathrm{c}}{\mathrm{b}} \mathrm{T}$, i.e.,
$\mathrm{u}_{\mathrm{m}} \propto \mathrm{T}$
$\therefore v_{\mathrm{m}}$ graph is linear w.r.t. temperature and the straingth line shown by line $\mathrm{B}$. Thus, option (D) is true.
