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Q.

Power radiated by a black body is $P_{0}$ and the wavelength corresponding to maximum energy is around $λ_{0}$ . On changing the temperature of the black body, it was observed that the power radiated becomes $\frac{256}{81} P_{0}$ . The shift in wavelength corresponding to the maximum energy will be

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a

$- \frac{λ_{0}}{4}$

b

$- \frac{λ_{0}}{2}$

c

$+ \frac{λ_{0}}{2}$

d

$+ \frac{λ_{0}}{4}$

answer is C.

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Detailed Solution

According to Wien's law $λ_{0} T_{0} = λ T$ , According to Stefan's law $\frac{P_{0}}{P} = {(\frac{T_{0}}{T})}^{4}$

As $P = \frac{256}{81} P_{0}$ $\Rightarrow$ $λ = \frac{3}{4} λ_{0}$

Therefore , Wavelength shift $∆ λ = - \frac{λ_{0}}{4}$

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