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A black body has maximum wavelength ' $\lambda_{\mathrm{m}}$ ' at temperature $2000 \mathrm{~K}$. Its corresponding wavelength at temperature $3000 \mathrm{~K}$ will be
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Verified Answer
The correct answer is:
$\frac{2 \lambda_m}{3}$
By Wien's displacement law, $\lambda \mathrm{T}=$ constant
$$
\begin{aligned}
& \therefore \lambda \propto \frac{1}{\mathrm{~T}} \\
& \frac{\lambda_2}{\lambda_1}=\frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{2000}{3000}=\frac{2}{3} \\
& \lambda_2=\frac{2}{3} \lambda_1
\end{aligned}
$$
$$
\begin{aligned}
& \therefore \lambda \propto \frac{1}{\mathrm{~T}} \\
& \frac{\lambda_2}{\lambda_1}=\frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{2000}{3000}=\frac{2}{3} \\
& \lambda_2=\frac{2}{3} \lambda_1
\end{aligned}
$$
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