First slide

Radiation

Question

When the temperature of a black body increases, it is observed that the wavelength corresponding to maximum energy changes from 0.13 $μ m$ to 0.26 $μm$ . The ratio of the emissive powers of the body at the respective temperature is:

Moderate

A

$\frac{16}{1}$
B

$\frac{4}{1}$
C

$\frac{1}{4}$
D

$\frac{1}{16}$

Solution

$λ_{1} T_{1} = λ_{2} T_{2}$
   $\frac{λ_{1}}{λ_{2}} = \frac{T_{2}}{T_{1}} = \frac{0.26}{0.13} = 2$
$T_{2} = 2 T_{1}$
By Stefan's law, emissive power E = ${σT}^{4}$
   $E_{1} = {σT}_{1}^{4}; E_{2} = {σT}_{2}^{4}$
   $\frac{E_{1}}{E_{2}} = \frac{{σT}_{1}^{4}}{{σT}_{2}^{4}} = \frac{{T_{1}}^{4}}{{(2 T_{1})}^{4}} = \frac{1}{16}$

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