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Q.

For maximum radiant energy from the moon, the corresponding wavelength is 14 micron. If Wien's constant is b = 2892 X $10^{- 6}$ mK, then temperature of the moon is

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a

207 K

b

270 K

c

270 ⁰C

d

207⁰C

answer is A.

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Detailed Solution

Given, $λ_{m} = 14 micron = 14 μ m = 14 \times 10^{- 6} m$

and Wien constant, $b = 2892 \times 10^{- 6} mK$

According to Wien's displacement law,

$λ_{m} = \frac{b}{T} or T = \frac{b}{λ_{m}} = \frac{2892 \times 10^{- 6} mK}{14 \times 10^{- 6} m}$

$∴ T = 206.6 K \approx 207 K$

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