A black body has maximum wavelength $\lambda_{\mathrm{m}}$ at temperature $2200 \mathrm{~K}$. Its…

A black body has maximum wavelength $\lambda_{\mathrm{m}}$ at temperature $2200 \mathrm{~K}$. Its corresponding wavelength at temperature $3300 \mathrm{~K}$ will be
  1. $\frac{9}{4} \lambda_{\mathrm{m}}$
  2. $\frac{3}{2} \lambda_{\mathrm{m}}$
  3. $\frac{4}{9} \lambda_{\mathrm{m}}$
  4. $\frac{2}{3} \lambda_{\mathrm{m}}$

Solution

$\lambda_{\mathrm{m}} \mathrm{T}=$ constant $\therefore \frac{\lambda_{\mathrm{m}}}{\lambda_{\mathrm{m}}}=\frac{\mathrm{T}}{\mathrm{T}^{\prime}}=\frac{2200}{3300}=\frac{2}{3}$ $\therefore \lambda_{\mathrm{m}}^{\prime}=\frac{2}{3} \lambda_{\mathrm{m}}$

Asked in: MHT CET 2020 (13 Oct Shift 1)

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