Question

A black body radiates maximum energy at wavelength ‘λ’ and its emissive power is ‘E’. Now due to change in temperature of that body, it radiates maximum energy at wavelength `(3λ)/4`. At that temperature emissive power is ______.

Options

• `81/16`

• `81/256`

• `16/81`

• `256/81`

Answer 1

A black body radiates maximum energy at wavelength ‘λ’ and its emissive power is ‘E’. Now due to change in temperature of that body, it radiates maximum energy at wavelength `(3λ)/4`. At that temperature emissive power is `bbunderline(256/81)`.

Explanation:

Emissive power of a black body is,

E = σT⁴

According to Wien’s displacement law,

`λ = b/T`

∴ E = `(σb^4)/(λ^4)`

∴ `E_2/E_1 = λ_1^4/λ_2^4`

∴ `E_2/E_1 = λ^4/((3λ)/4)^4`

= `λ^4/((81λ^4)/256)`

= `λ^4 xx 256/(81λ^4)`

= `256/81`