The radiation energy density per unit wavelength at temperature $T$ is maximum at a wavelength $\lambda_0$.…

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
  1. $\frac{\lambda_0}{4}$
  2. $2 \lambda_0$
  3. $4 \lambda_0$
  4. $\frac{\lambda_0}{2}$

Solution

According to Wien's displacement law, $\lambda_m T=$ constant. $\begin{aligned} & \therefore \lambda_{\mathrm{m}} \times T=\lambda^{\prime} \times T^{\prime} \\ & \Rightarrow \lambda_0 T=\lambda^{\prime} \times 2 T \\ & \Rightarrow \lambda^{\prime}=\frac{\lambda_0}{2}\end{aligned}$

Asked in: MHT CET 2022 (06 Aug Shift 2)

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