Sun radiates thermal radiation with maximum intensity at the wavelength λ$$=0.5$$ μm while its surface temperature is $$6000$$ K. If sun cools down to a temperature where it emits only $$81$$% of its present power, the maximum intensity will then be emitted at wavelength λ' $$(in$$ micro metre $$)is$$ equal to $$10=3.1622$$

Question

Sun radiates thermal radiation with maximum intensity at the wavelength  λ$$=0.5$$ μm while its surface temperature is  $$6000$$ K. If sun cools down to a temperature where it emits only $$81$$% of its present power, the maximum intensity will then be emitted at wavelength λ'  $$(in$$ micro metre $$)is$$ equal to  $$10=3.1622$$

Infinity Learn · Accepted Answer

$$1$$. When sun cools to the temperature T where it emits only $$81$$% of its present radiating power, thenσ$$T4=81100$$σ$$60004$$∵$$E=$$σ$$T4$$   σ$$=5.67x$$ $$10-8$$ unit⇒$$T=0.96000$$ $$=0.95$$×$$6000=5700$$ K $$2$$. By Wien’s displacement law,  λ$$mT=constantHence$$ if  λm is the required wavelength  λ$$m5700=0.5$$×$$6000$$λ$$m=60005700$$×$$0.5=1019=0.53$$ μm Therefore, the correct answer is $$0.53$$

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