Question

The power radiated by a black body is $P$ and it radiates maximum energy around the wavelength ${\lambda }_o$ . If the temperature of the black body is now changed so that it radiates maximum energy around a wavelength $3{\lambda }_o/4$ , the power radiated by it will increase by a factor of :

• A. $4/3$
• B. $16/9$
• C. $64/27$
• D. $256/81$

Answer 1

The correct option is D $256/81$

From Wein's displacement law, we know that ${\lambda }_{max}T=CONSTANT$

So, let us assume that initial temperature of the body be $T_1$

and by changing the temperature from $T_{1}toT$, wavelength will change from $\lambda$ to $\frac{3\lambda }{4}$,so applying the above relation,

${\lambda }_0{T}_1=\frac{3{\lambda }_0}{4}T$

Hence, $T=\frac{4}{3}{T}_1$

and we know that $P=e{T}^4$

So, $P^{\prime }=\frac{256}{81}P$