Discussion
The peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 1.45 µm. If the peak wavelength of emitted radiation changes to 2.90 µm, then the temperature (in K) of the black body is
Answer: B
The temperature is 1000 K.
Wien's displacement law says the peak wavelength is inversely proportional to absolute temperature, \(\lambda_{\max}T = \text{constant}\):
\[ \begin{aligned} T_{2} &= T_{1}\frac{\lambda_{1}}{\lambda_{2}} \\ &= 2000 \times \frac{1.45}{2.90} = 1000\ \text{K} \end{aligned} \]
The constant here is 1.45 × 2000 = 2900 µm K, the familiar Wien constant. Doubling the peak wavelength halves the temperature; 4000 K treats the relation as direct, and 500 K and 8000 K square the ratio, as if confusing it with a power law.
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