Q152 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Physics

A body at \(3000 \mathrm{~K}\) emits maximum energy at a wavelength of \(9660 Å\). If the sun emits maximum energy at a wavelength of \(4950 Å\), what would be the temperature of the sun?

  • Correct answer
    A
    \(5855 \mathrm{~K}\)
  • B
    \(7000 \mathrm{~K}\)
  • C
    \(4250 \mathrm{~K}\)
  • D
    \(8000 \mathrm{~K}\)

Solution

Temperature of body, \(T_1=3000 \mathrm{~K}\) Body emits maximum energy at wavelength, \(\lambda_1=9660 Å\) Wavelength of radiation emitted by sun, \(\lambda_2=4950 Å\) Sun's temperature, \(T_2=\) ? According to Wien's displacement law, \(\begin{array}{ll} \lambda & \propto \frac{1}{T} \\ \Rightarrow \quad \lambda & =\frac{b}{T}[b=\text { Constant of } \end{array}\) proportionality] \(\begin{array}{llll} \Rightarrow & \frac{\lambda_1}{\lambda_2} =\frac{T_2}{T_1} \\ \Rightarrow & T_2 =\frac{T_1 \lambda_1}{\lambda_2} =\frac{3000 \times 9660}{4950} \\ & =5854.5 \mathrm{~K} \approx 5855 \mathrm{~K} \end{array}\)

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

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