The wavelength of maximum intensity of radiation emitted by a star is $289.8 \mathrm{~nm}$. The radiation intensity of the star is (Stefan's constant $=5.67 imes 10^{-8} \mathrm{Wm}^2 \mathrm{~K}^{-4}$, constant $b=2898 \mu \mathrm{mK}$ )

Question

The wavelength of maximum intensity of radiation emitted by a star is $289.8 \mathrm{~nm}$. The radiation intensity of the star is (Stefan's constant $=5.67 	imes 10^{-8} \mathrm{Wm}^2 \mathrm{~K}^{-4}$, constant $b=2898 \mu \mathrm{mK}$ )

Aicharya · Accepted Answer

$\lambda_m=289.8 \mathrm{~nm}=289.8 	imes 10^{-9} \mathrm{~m}$ From Wein's law, $\begin{aligned} & \lambda_m T=b \quad 	ext { (constant) } \ & 	ext { Temperature of star, } T=\frac{b}{\lambda_m}=\frac{2898 	imes 10^{-6}}{289.8 	imes 10^{-9}} \ & =\frac{2898 	imes 10^{-6}}{2898 	imes 10^{-10}} \ & =10^4 \mathrm{~K} \ & 	ext { Radiation intensity } E=\sigma T^4 \ & =5.67 	imes 10^{-8}\left(10^4ight)^4 \ & =5.67 	imes 10^{-8} 	imes 10^{16} \ & =5.67 	imes 10^8 \mathrm{~W} / \mathrm{m}^2 \ & \end{aligned}$

The wavelength of maximum intensity of radiation emitted by a star is $289.8 \mathrm{~nm}$. The radiation…

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