A body at \(3000 \mathrm{~K}\) emits maximum energy at a wavelength of \(9660 Å\). If the sun emits maximum…
A body at \(3000 \mathrm{~K}\) emits maximum energy at a wavelength of \(9660 Å\). If the sun emits maximum energy at a wavelength of \(4950 Å\), what would be the temperature of the sun?
\(5855 \mathrm{~K}\)
\(7000 \mathrm{~K}\)
\(4250 \mathrm{~K}\)
\(8000 \mathrm{~K}\)
Solution
Temperature of body, \(T_1=3000 \mathrm{~K}\)
Body emits maximum energy at wavelength,
\(\lambda_1=9660 Å\)
Wavelength of radiation emitted by sun,
\(\lambda_2=4950 Å\)
Sun's temperature, \(T_2=\) ?
According to Wien's displacement law,
\(\begin{array}{ll}
\lambda & \propto \frac{1}{T} \\
\Rightarrow \quad \lambda & =\frac{b}{T}[b=\text { Constant of }
\end{array}\)
proportionality]
\(\begin{array}{llll}
\Rightarrow & \frac{\lambda_1}{\lambda_2} =\frac{T_2}{T_1} \\
\Rightarrow & T_2 =\frac{T_1 \lambda_1}{\lambda_2} =\frac{3000 \times 9660}{4950} \\
& =5854.5 \mathrm{~K} \approx 5855 \mathrm{~K}
\end{array}\)