MHT CET · Physics · Thermal Properties of Matter
The radiation energy density per unit wavelength at temperature \(T\) is maximum at a wavelength \(\lambda_0\). At temperature \(2 T\), it will have a maximum at a wavelength
- A \(\frac{\lambda_0}{4}\)
- B \(2 \lambda_0\)
- C \(4 \lambda_0\)
- D \(\frac{\lambda_0}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{\lambda_0}{2}\)
Step-by-step Solution
Detailed explanation
According to Wien's displacement law, \(\lambda_m T=\) constant.
\(\begin{aligned} & \therefore \lambda_{\mathrm{m}} \times T=\lambda^{\prime} \times T^{\prime} \\ & \Rightarrow \lambda_0 T=\lambda^{\prime} \times 2 T \\ & \Rightarrow \lambda^{\prime}=\frac{\lambda_0}{2}\end{aligned}\)
\(\begin{aligned} & \therefore \lambda_{\mathrm{m}} \times T=\lambda^{\prime} \times T^{\prime} \\ & \Rightarrow \lambda_0 T=\lambda^{\prime} \times 2 T \\ & \Rightarrow \lambda^{\prime}=\frac{\lambda_0}{2}\end{aligned}\)
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