Three discs $A, B$ and $C$ having radii $2\; m, 4\;m,$ and $6 \;m$, respectively are coated with carbon black on their outer surfaces. The wavelengths corresponding to maximum intensity are $300\; nm, 400\; nm$ and $500\; nm$, respectively. The power radiated by them are $Q_A,Q_B$ and $Q_C$ respectively.
IIT 2004, Diffcult
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(b) Radiated power$P = A\varepsilon \sigma {T^4}$
==> P$ \propto A{T^4}$
From Wein’s law, ${\lambda _m}T = $constant
==> $T \propto \frac{1}{{{\lambda _m}}}$
$P \propto \frac{A}{{{{({\lambda _m})}^4}}} \propto \frac{{{r^2}}}{{{{({\lambda _m})}^4}}}$
==> ${Q_A}:{Q_B}:{Q_C} = \frac{{{2^2}}}{{{{(300)}^4}}}:\frac{{{4^2}}}{{{{(400)}^4}}}:\frac{{{6^2}}}{{{{(500)}^4}}}$
${Q_B}$ will be maximum.
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