When the temperature of a blackbody is doubled the maximum value of its spectral energy density with respect to that at initial temperature would become?

Q)

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Option 3 : Reduced to half

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CONCEPT:

• The Wien's displacement law states that- the black-body radiation curve for different temperatures will give the maximum wavelength at particular temperature and that is inversely proportional to the temperature.

So \({\lambda _m}\;T = b\) ⇒ \(T = \frac{b}{{{\lambda _m}}}\)

Where λ = wavelength, T = temperature, b = Wien’s constant

EXPLANATION:

• From the above formula, the maximum wavelength is inversely proportional to the temperature. If the temperature is doubled then the wavelength of the radiation will reduced to half. So option 3 is correct.

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Text Solution

doubledhalvedunchangedquadrupled

Answer : A

Solution : (i) `lamda_(m)`T = constant <br> `thereforeTC/v` = constant <br> `therefore(T_(1)C)/v_(1)=(2T_(1)C)/v_(2)` <br> `thereforev_(2)=2v_(1)` <br> (ii) `lamdaprop1/T` but `lamdaprop1/v" "thereforevpropT` <br> `therefore` If T is doubled, v is doubled.