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In a certain planetary system, it is observed that one of the celestial bodies having a surface temperature of 200 K, emits radiation of maximum intensity near the wavelength $12 μ m$ . The surface temperature of a nearby star which emits light of maximum intensity at a wavelength $λ = 4800 \overset{o}{A}$ , is :

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5000 K

2500 K

7500 K

10000 K

answer is A.

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Detailed Solution

$\begin{array}{l} λ_{m} T = constant \\ λ_{1} T_{1} = λ_{2} T_{2} \\ 12 μm \times 200= (4800 \overset{o}{A}) T \\ T = \frac{12 \times 10^{- 6} \times 200}{4800 \times 10^{- 10}} = 5000 K \end{array}$

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