MHT CET · Physics · Thermal Properties of Matter
A black body has maximum wavelength ' \(\lambda_{\mathrm{m}}\) ' at temperature \(2000 \mathrm{~K}\). Its corresponding wavelength at temperature \(3000 \mathrm{~K}\) will be
- A \(\frac{4 \lambda_m}{9}\)
- B \(\frac{2 \lambda_m}{3}\)
- C \(\frac{3 \lambda_{\mathrm{m}}}{2}\)
- D \(\frac{9}{4} \lambda_m\)
Answer & Solution
Correct Answer
(B) \(\frac{2 \lambda_m}{3}\)
Step-by-step Solution
Detailed explanation
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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