Question

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

• A. $\frac{4}{3}$
• B. $\frac{16}{9}$
• C. $\frac{64}{27}$
• D. $\frac{256}{81}$

Answer 1

The correct option is D $\frac{256}{81}$

From Stefan-Boltzmann law
Power $P\propto T^4$

From Wein's law
$T\propto \frac{1}{{\lambda }_m}$

$\therefore P\propto \frac{1}{{\lambda }_m^4}$

$\Rightarrow P{\lambda }_m^4=C$ (Constant)

$\therefore P{\lambda }_0^4=P_f{\left(\frac{3{\lambda }_o}{4}\right)}^4$

$P_f=\frac{256}{81}P$