The wavelength of maximum solar emission is observed to be approximately 0.475 μm. What is the surface temperature of the sun (assumed as blackbody)?
The wavelength of maximum solar emission is observed to be approximately 0.475 μm. What is the surface temperature of the sun (assumed as blackbody)?
Related questions
Question
![### Determining the Surface Temperature of the Sun
The wavelength of maximum solar emission is observed to be approximately 0.475 µm. To determine the surface temperature of the sun (assuming it acts as a blackbody), we use Wien's Law, which states:
\[ \lambda_{max} T = b \]
Where:
- \(\lambda_{max}\) is the wavelength of maximum emission,
- \(T\) is the absolute temperature in Kelvins (K),
- \(b\) is Wien's displacement constant, approximately \(2.897 \times 10^{-3}\) m·K.
Given:
\[ \lambda_{max} = 0.475 \times 10^{-6} \text{ m} \]
Rearranging Wien's Law to solve for temperature:
\[ T = \frac{b}{\lambda_{max}} \]
Plug in the values:
\[ T = \frac{2.897 \times 10^{-3} \text{ m·K}}{0.475 \times 10^{-6} \text{ m}} \]
\[ T ≈ 6099 \text{ K} \]
Thus, the surface temperature of the sun is approximately 6099 Kelvin.
This calculation assumes that the sun behaves as an ideal blackbody, which is an object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbdf4ad1c-8d6e-4c6e-ab0d-20fae6a9f061%2F32c9e077-3a47-4c6c-b082-4f14bfae986b%2Ftznofr_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining the Surface Temperature of the Sun
The wavelength of maximum solar emission is observed to be approximately 0.475 µm. To determine the surface temperature of the sun (assuming it acts as a blackbody), we use Wien's Law, which states:
\[ \lambda_{max} T = b \]
Where:
- \(\lambda_{max}\) is the wavelength of maximum emission,
- \(T\) is the absolute temperature in Kelvins (K),
- \(b\) is Wien's displacement constant, approximately \(2.897 \times 10^{-3}\) m·K.
Given:
\[ \lambda_{max} = 0.475 \times 10^{-6} \text{ m} \]
Rearranging Wien's Law to solve for temperature:
\[ T = \frac{b}{\lambda_{max}} \]
Plug in the values:
\[ T = \frac{2.897 \times 10^{-3} \text{ m·K}}{0.475 \times 10^{-6} \text{ m}} \]
\[ T ≈ 6099 \text{ K} \]
Thus, the surface temperature of the sun is approximately 6099 Kelvin.
This calculation assumes that the sun behaves as an ideal blackbody, which is an object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
