Question

A black body is at a temperature of $2880K.$ The energy of radiation emitted by this object with wavelength between $499nm$ and $500nm$ is $u_{1,}$ between $999nm$ with $1000nm$ is $u_2$ and between $1499nm$ and $1500nm$ is $u_{3.}$ The Weins constant is $b=0.28cmK.$ The correct alternative is

• A. $u_1>u_2$
• B. $u_1=0$
• C. $u_3=0$
• D. $u_2>u_1$

Answer 1

The correct option is D $u_2>u_1$

$T=2880K$
$b=0.28cmK$
$=28\times {10}^{-4}m,K$
From Wiens displacement law,
$\lambda T=b$

${\Rightarrow \lambda }_m=\frac{b}{T}=\frac{28\times {10}^{-4}}{2880}\text{m}$
$\underset{–}{\sim }{10}^{-6}\text{m}$
$\underset{–}{\sim }1000\times {10}^{-9}\text{m}$
$=1000nm$
i.e., maximum energy is radiated through the wavelength between $999nm$ and $1000nm.$
$\therefore u_2>u_1$