(A) According to Wien's displacement law,$\lambda_{\max} T = b$.Given $\lambda_{\max} = 289.8 \, nm = 289.8 \times 10^{-9} \, m$ and $b = 2898 \, \mu

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(A) According to Wien's displacement law,$\lambda_{\max} T = b$.Given $\lambda_{\max} = 289.8 \, nm = 289.8 \times 10^{-9} \, m$ and $b = 2898 \, \mu m \cdot K = 2898 \times 10^{-6} \, m \cdot K$.Calculating the temperature $T$:$T = \frac{b}{\lambda_{\max}} = \frac{2898 \times 10^{-6}}{289.8 \times 10^{-9}} = 10 \times 10^3 = 10^4 \, K$.According to Stefan-Boltzmann Law,the radiation intensity (emissive power) $E$ is given by $E = \sigma T^4$.Substituting the values:$E = (5.67 \times 10^{-8}) \times (10^4)^4 = 5.67 \times 10^{-8} \times 10^{16} = 5.67 \times 10^8 \, W/m^2$.

Class 11 Physics 10-2.Heat Transfer Spectral Emissive Power and Wien's Displacement Law

Medium

The wavelength of maximum intensity of radiation emitted by a star is $289.8 \, nm$. The radiation intensity for the star is: (Stefan's constant $\sigma = 5.67 \times 10^{-8} \, W m^{-2} K^{-4}$,Wien's constant $b = 2898 \, \mu m \cdot K$)

A
$5.67 \times 10^8 \, W/m^2$
B
$5.67 \times 10^{12} \, W/m^2$
C
$10.67 \times 10^7 \, W/m^2$
D
$10.67 \times 10^{14} \, W/m^2$

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10-2.Heat Transfer

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Spectral Emissive Power and Wien's Displacement Law

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The wavelength of maximum intensity of radiation emitted by a star is $289.8 \, nm$. The radiation intensity for the star is: (Stefan's constant $\sigma = 5.67 \times 10^{-8} \, W m^{-2} K^{-4}$,Wien's constant $b = 2898 \, \mu m \cdot K$)

Similar Questions

$A$ black body emits radiation of maximum intensity at wavelength $\lambda$ at temperature $T \ K$. Its corresponding wavelength at temperature $1.5 \ T \ K$ will be

The surface temperature of the sun, which has maximum energy emission at $500 \, nm$, is $6000 \, K$. The temperature of a star, which has maximum energy emission at $400 \, nm$, will be ........ $K$.

$A$ particular star (assuming it as a black body) has a surface temperature of about $5 \times 10^4 \ K$. The wavelength in nanometers at which its radiation becomes maximum is $(b = 0.0029 \ mK)$.

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