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Question

(A) According to Wien's displacement law, $\lambda_{max} T = b$, where $b = 2.9 	imes 10^{-3} m K$ is Wien's constant.Given $\lambda_{max} = 2900 Å =

Vedclass · Accepted Answer

$5.67 	imes 10^8 W m^{-2}$

Vedclass · Answer

(A) According to Wien's displacement law, $\lambda_{max} T = b$, where $b = 2.9 	imes 10^{-3} m K$ is Wien's constant.Given $\lambda_{max} = 2900 Å = 2900 	imes 10^{-10} m = 2.9 	imes 10^{-7} m$.Substituting the values, $T = \frac{b}{\lambda_{max}} = \frac{2.9 	imes 10^{-3}}{2.9 	imes 10^{-7}} = 10^4 K$.The intensity of radiation emitted by a perfect radiator (black body) is given by the Stefan-Boltzmann law: $E = \sigma T^4$.Given $\sigma = 5.67 	imes 10^{-8} W m^{-2} K^{-4}$.$E = (5.67 	imes 10^{-8}) 	imes (10^4)^4 = 5.67 	imes 10^{-8} 	imes 10^{16} = 5.67 	imes 10^8 W m^{-2}$.Thus, the correct option is $A$.

If the radiation emitted by a perfect radiator has maximum intensity at a wavelength of $2900 Å$, the intensity of radiation emitted by it is (Stefan-Boltzmann's constant $= 5.67 \times 10^{-8} W m^{-2} K^{-4}$ and Wien's constant $= 2.9 \times 10^{-3} m K$).

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