Two spherical bodies A(radius 6 cm) and B(radius 18 cm) are at temperature T1 and T2, 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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Two spherical bodies A(radius 6 cm) and B(radius 18 cm) are at temperature T₁ and T₂, 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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u = 6AT⁴

^{$\frac{u_{A}}{u_{B}} = \frac{A_{A} T_{A}^{4}}{A_{B} T_{B}^{4}}$}

^{$\frac{T_{A}}{T_{B}} = \frac{λ_{B}}{λ_{A}} = 3$}

^{$\frac{u_{A}}{u_{B}} = \frac{A_{A}}{A_{B}} (81) = {(\frac{r_{A}}{r_{B}})}^{2} (81)$}

^{$(\frac{r_{A}}{r_{B}}) = \frac{1}{3}$}

^{$\frac{u_{A}}{u_{B}} = 9$}

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