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Two spherical bodies A of radius 6 cm and B of radius 18 cm are at temperature $T_{1} {and T}_{2},$ respectively. The maximum intensity in the emission spectrum of A is at 500 nm and in that of B is at 1500 nm. Considering them to be black bodies, what will be the ratio of the rate of total energy radiated by A to that of B ?

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answer is B.

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Detailed Solution

$λ_{1} T_{1} = λ_{2} T_{2} \Rightarrow \frac{T_{1}}{T_{2}} = \frac{λ_{2}}{λ_{1}}$

$P \propto r^{2} T^{4}$

$\frac{P_{1}}{P_{2}} = {(\frac{r_{1}}{r_{2}})}^{2} {(\frac{T_{1}}{T_{2}})}^{4} = {(\frac{r_{1}}{r_{2}})}^{2} {(\frac{λ_{2}}{λ_{1}})}^{4}$

$= {(\frac{6}{18})}^{2} {(\frac{1500}{500})}^{4} = {(\frac{1}{3})}^{2} {(\frac{3}{1})}^{4}$

$= 3^{2} = 9$

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