Q130 / 150 · MHT CET 2021 (21 Sep Shift 1) · Physics

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
    $\frac{4 \lambda_m}{9}$
  • Correct answer
    B
    $\frac{2 \lambda_m}{3}$
  • C
    $\frac{3 \lambda_{\mathrm{m}}}{2}$
  • D
    $\frac{9}{4} \lambda_m$

Solution

By Wien's displacement law, $\lambda \mathrm{T}=$ constant $$ \begin{aligned} & \therefore \lambda \propto \frac{1}{\mathrm{~T}} \\ & \frac{\lambda_2}{\lambda_1}=\frac{\mathrm{T}_1}{\mathrm{~T}_2}=\frac{2000}{3000}=\frac{2}{3} \\ & \lambda_2=\frac{2}{3} \lambda_1 \end{aligned} $$

Hence, the correct answer is option: 'B'.

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