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The power radiated by a black body is P and it radiates maximum energy around the wavelength $λ_{0}$ . Now the temperature of the black body is changed so that it radiates maximum energy around wavelength $λ_{0} / 2$ . The power radiated by it will now increase by a factor of

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answer is 16.

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Detailed Solution

Power $P α T^{4}, T α \frac{1}{λ}$ $P α \frac{1}{λ^{4}} \Rightarrow \frac{P_{2}}{P_{1}} = {(\frac{λ_{1}}{λ_{2}})}^{4}$ $\frac{P_{2}}{P} = {(\frac{λ_{0}}{\frac{λ_{0}}{2}})}^{4}$ $\frac{P_{2}}{P} = 2^{4} \Rightarrow P_{2} = 16 P$

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