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 $$12$$μm. The surface temperature of a nearby star which emits light of maximum intensity at a wavelength λ$$=4800$$ Ao,is :

Question

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 $$12$$μm. The surface temperature of a nearby star which emits light of maximum intensity at a wavelength λ$$=4800$$ Ao,is :

Infinity Learn · Accepted Answer

λ$$mT=constant$$λ$$1T1$$   $$=$$    λ$$2T212$$μm  × $$200=$$   $$4800$$  $$AoTT=12$$  ×  $$10$$−$$6$$  ×  $$2004800$$  ×  $$10$$−$$10$$  $$=$$  $$5000$$  K

Radiation

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

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Radiation

Remember concepts with our Masterclasses.

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 12μm. The surface temperature of a nearby star which emits light of maximum intensity at a wavelength λ=4800 Ao,is :

λmT=constantλ1T1 = λ2T212μm × 200= 4800 AoTT=12 × 10−6 × 2004800 × 10−10 = 5000 K

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free study material

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