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A distant star has its surface temperature of about 2898 K. The wavelengths of light radiation which has maximum intensity emitted from these stars i.e. \(\lambda_{max}\) =

  • A.289.8 nm
  • B.1000 nm
  • C.10000 nm
  • D.550 nm

Answer: B

The peak wavelength is 1000 nm.

Wien's displacement law gives the wavelength of maximum emission of a black body:

\[ \begin{aligned} \lambda_{max} &= \frac{b}{T} = \frac{2.898 \times 10^{-3}\ \text{m K}}{2898\ \text{K}} \\ &= 10^{-6}\ \text{m} \end{aligned} \]

That is 1000 nm, in the near infrared. The temperature was chosen so the numbers cancel.

289.8 nm would need a star ten times hotter, and 10000 nm a body ten times cooler; 550 nm is the peak of the Sun, at about 5800 K.

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