Question

A black body radiates maximum energy around the wavelength ${\lambda }_0$. lf the temperature of the black body is changed so that it radiates maximum energy around the wavelength $2{\lambda }_0$, the ratio of power radiated now to power radiated previously is :

• A. $\frac{3}{4}$
• B. $\frac{27}{64}$
• C. $\frac{1}{16}$
• D. $\frac{9}{16}$

Answer 1

The correct option is C $\frac{1}{16}$

By wein's displacement law, $T{\lambda }_{max}=b$

Hence, $T{\lambda }_0=T^{\prime }\left({2\lambda }_0\right)$

$T^{\prime }=\frac{T}{2}$

Since, by stephan boltzman law, $P=\sigma A{T}^4$

$\frac{P_2}{P_1}=\frac{T^{\prime 4}}{T^4}=\frac{1}{16}$

Answer is option C.