A spherical blackbody of radius 10\ m is maintained at a...

According to the Stefan-Boltzmann law, the radiated power is $P = \sigma A T^4 = \sigma (4\pi R^2) T^4$.

For the new state, $P' = 16P and R' = \dfrac{R}{2}$.

$16P = \sigma \left(4\pi \left(\dfrac{R}{2}\right)^2\right) (T')^4$

$16P = \dfrac{1}{4} \sigma (4\pi R^2) (T')^4$

$16P = \dfrac{1}{4} P \left(\dfrac{T'}{T}\right)^4$

\left(\dfrac{T'}{T}\right)^4 = 64$<br><br>$T' = (64)^{1/4} T = 2\sqrt{2} T$<br><br>According to Wien's displacement law,$\lambda_m T = \text{constant}$.<br><br>$\lambda_m' T' = \lambda_m T$<br><br>$\lambda_m' = \lambda_m \left(\dfrac{T}{T'}\right) = 5000 \times \dfrac{1}{2\sqrt{2}} = \dfrac{2500}{\sqrt{2}}\ \text{\AA}$<br><br>Answer:$\dfrac{2500}{\sqrt{2}}\ Å