An exoplanet has a surface temperature of 1,433.2 K. Assuming the exoplanet radiates as a thermal radiator, what is the peak wavelength (in nanometer) of the emission? Use two significant figures in your answer.




We can use **Wien's displacement law** to find the peak wavelength (\(\lambda_{\text{peak}}\)) of the radiation emitted by a thermal radiator:

\[
\lambda_{\text{peak}} = \frac{b}{T}
\]

where:
- \(b\) is Wien's displacement constant, approximately \(2.897 \times 10^6 \, \text{nm} \cdot \text{K}\),
- \(T\) is the surface temperature of the object (in this case, 1433.2 K).

Now, let's compute the peak wavelength:

\[
\lambda_{\text{peak}} = \frac{2.897 \times 10^6 \, \text{nm} \cdot \text{K}}{1433.2 \, \text{K}} 
\]

Calculating that:

\[
\lambda_{\text{peak}} = 2022.5 \, \text{nm}
\]

Rounding to two significant figures, the peak wavelength is:

\[
\lambda_{\text{peak}} \approx 2000 \, \text{nm}
\]

Thus, the peak wavelength of the exoplanet's emission is approximately **2000 nm**.

Would you like more details on this calculation, or have any other questions?

Here are 5 related questions:
1. How does Wien's law apply to blackbody radiation?
2. What is the relationship between temperature and radiation wavelength?
3. How do astronomers detect exoplanets using their emitted radiation?
4. What type of radiation corresponds to a wavelength of 2000 nm?
5. How does the peak wavelength vary with different temperatures?

**Tip:** Lower temperatures result in longer peak wavelengths, typically in the infrared region.

An exoplanet has a surface temperature of 1,433.2 K. Assuming the exoplanet radiates as a thermal radiator, what is the peak wavelength (in nanometer) of the emission? Use two significant figures in your answer.

Learn how to calculate the peak wavelength of radiation emitted by an exoplanet with a surface temperature of 1,433.2 K using Wien's displacement law. This problem applies thermodynamic concepts and the Wien's law formula to find the peak wavelength at approximately 2000 nm. Suitable for Grades 10-12 students studying thermal radiation.

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