Question

A hot black body emits the energy at the rate of 16 J $m^{-}2s^{-1}$ and its most intense radiation corresponds to 20,000 A. When the temperature of this body is further increased and its most intense radiation corresponds to 10,000 A, then find the value of energy radiated in $J{m}^{-}2S^{-1}$

• A. 64 J $m^{-2}{s}^{-1}$
• B. 128 J $m^{-2}{s}^{-1}$
• C. 256 J $m^{-2}{s}^{-1}$
• D. 108 J $m^{-2}{s}^{-1}$

Answer 1

The correct option is C 256 J $m^{-2}{s}^{-1}$

Wein's displacement law is :
${\lambda }_{m}T=bi.e.T\propto \frac{1}{{\lambda }_m}$
Here, ${\lambda }_m$ becomes half.
$\therefore$ Temperature doubles.
Also$E=\sigma T^4\Rightarrow \frac{E_1}{E_1}={\left(\frac{T_1}{T_2}\right)}^4\Rightarrow E_2={\left(\frac{T_2}{T_1}\right)}^4{e}_1=(2{)}^4.16$
= 16.16 = 256 J $m^{-2}{s}^{-1}$