The power radiated by a black body is P and it radiates maximum energy at wavelength, $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\dfrac{3}{4}\lambda_0$, 4 the power radiated by it becomes nP. The value of n is
$\dfrac{256}{81}$
$\dfrac{4}{3}$
$\dfrac{3}{4}$
$\dfrac{81}{256}$
Explanation:
We know,
$\lambda_{max} T= constant (Wiens law)$
So, $\lambda_{max_1} T_1=\lambda_{max_2} T_2$
$\Rightarrow \lambda_0 T=\dfrac{3 \lambda_0}{4}\acute{T}$
$\Rightarrow \acute{T} =\dfrac{4}{3}T$
$ So, \dfrac{P_2}{P_1}= \left(\dfrac{\acute{T}}{T}\right)^4=\left(\dfrac{4}{3}\right)^4=\dfrac{256}{81}$
We know,
$\lambda_{max} T= constant (Wiens law)$
So, $\lambda_{max_1} T_1=\lambda_{max_2} T_2$
$\Rightarrow \lambda_0 T=\dfrac{3 \lambda_0}{4}\acute{T}$
$\Rightarrow \acute{T} =\dfrac{4}{3}T$
$ So, \dfrac{P_2}{P_1}= \left(\dfrac{\acute{T}}{T}\right)^4=\left(\dfrac{4}{3}\right)^4=\dfrac{256}{81}$
