The Sun emits light with a maximum wavelength | vedclass

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(B) According to Wien's displacement law,the wavelength corresponding to maximum emission intensity is inversely proportional to the absolute temperat

Vedclass · Accepted Answer

$0.68$

Vedclass · Answer

(B) According to Wien's displacement law,the wavelength corresponding to maximum emission intensity is inversely proportional to the absolute temperature of the black body: $\lambda_{max} \propto \frac{1}{T}$.Let $T_S$ and $\lambda_S$ be the temperature and maximum wavelength of the Sun,and $T_X$ and $\lambda_X$ be the temperature and maximum wavelength of star $X$.Given: $\lambda_S = 510 \, nm$ and $\lambda_X = 350 \, nm$.The ratio of the temperatures is given by: $\frac{T_S}{T_X} = \frac{\lambda_X}{\lambda_S}$.Substituting the values: $\frac{T_S}{T_X} = \frac{350}{510} \approx 0.686$.Rounding to two decimal places,the ratio is $0.68$.

The Sun emits light with a maximum wavelength of $510 \, nm$,while another star $X$ emits light with a maximum wavelength of $350 \, nm$. What is the ratio of the surface temperature of the Sun to that of star $X$?

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