Question
Since we cannot physically collect data from stars and most other objects in the universe, almost all of the information we obtain from the universe comes from analyzing the light, or spectra, from those objects.The study of light is known as spectroscopy.As we have seen in this simulation, every blackbody emits light with an easily identified pattern known as the blackbody curve. This is the particular way the total light emitted by a blackbody varies with its frequency. The exact form of the curve depends only on the body’s temperature. Since we can treat stars as blackbodies, this is incredibly useful in astronomy that shows us that the color of a star is also indicative of its temperature.Use the simulation to determine the surface temperature of the following star:
Betelgeuse is a red supergiant star in the constellation Orion.
Knowing that Betelgeuse has peak intensity in the red and infrared wavelengths, adjust the intensity scale and temperature until you can determine the approximate surface temperature of the star.
1500 K
3500 K
5500 K
7500 K
Betelgeuse is a red supergiant star in the constellation Orion.
Knowing that Betelgeuse has peak intensity in the red and infrared wavelengths, adjust the intensity scale and temperature until you can determine the approximate surface temperature of the star.
1500 K
3500 K
5500 K
7500 K
Answers
GPT-4o mini
Betelgeuse, a red supergiant star, emits peak intensity in the red and infrared regions of the spectrum. Based on the characteristics of blackbody radiation, we can use Wien's displacement law, which states that the wavelength (\(\lambda_{max}\)) at which the intensity is at its peak is inversely proportional to the temperature (T) of the blackbody. The formula is:
\[
\lambda_{max} = \frac{b}{T}
\]
Where \(b\) is Wien's displacement constant, approximately equal to \(2898\, \mu m \cdot K\).
Since Betelgeuse shows peak intensity in the red and infrared wavelengths, we can estimate its surface temperature by observing where its peak brightness lies on the spectrum.
Given the temperature options (1500 K, 3500 K, 5500 K, and 7500 K):
- A temperature of 1500 K would correspond to peak wavelengths in the infrared range, which is too cool for Betelgeuse.
- A temperature of 3500 K would put the peak in the red but still in the cooler part of the spectrum.
- A temperature of 5500 K corresponds to the Sun's surface temperature and would place the peak in the green-yellow part of the spectrum, which is not appropriate for a red supergiant.
- A temperature of 7500 K would shift the peak even further toward the blue.
The most appropriate estimate for Betelgeuse, based on its description as a red supergiant with peak intensity in the red and infrared wavelengths, is likely around 3500 K. Thus, the approximate surface temperature of Betelgeuse is **3500 K**.
\[
\lambda_{max} = \frac{b}{T}
\]
Where \(b\) is Wien's displacement constant, approximately equal to \(2898\, \mu m \cdot K\).
Since Betelgeuse shows peak intensity in the red and infrared wavelengths, we can estimate its surface temperature by observing where its peak brightness lies on the spectrum.
Given the temperature options (1500 K, 3500 K, 5500 K, and 7500 K):
- A temperature of 1500 K would correspond to peak wavelengths in the infrared range, which is too cool for Betelgeuse.
- A temperature of 3500 K would put the peak in the red but still in the cooler part of the spectrum.
- A temperature of 5500 K corresponds to the Sun's surface temperature and would place the peak in the green-yellow part of the spectrum, which is not appropriate for a red supergiant.
- A temperature of 7500 K would shift the peak even further toward the blue.
The most appropriate estimate for Betelgeuse, based on its description as a red supergiant with peak intensity in the red and infrared wavelengths, is likely around 3500 K. Thus, the approximate surface temperature of Betelgeuse is **3500 K**.