White dwarfs have a temperature of 100×103 K. Calculate the maximum wavelength of a White dwarf.
White dwarfs have a temperature of 100×103 K. Calculate the maximum wavelength of a White dwarf.
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![**Question:**
White dwarfs have a temperature of \(100 \times 10^3\) K. Calculate the maximum wavelength of a white dwarf.
**Explanation:**
White dwarfs are a type of stellar remnant that are known for their high temperatures and typically exhibit temperatures in the range highlighted in the question. To determine the maximum wavelength (\(\lambda_{\text{max}}\)) emitted by a white dwarf, we can utilize Wien's Displacement Law. This law states:
\[ \lambda_{\text{max}} = \frac{b}{T} \]
where:
- \(\lambda_{\text{max}}\) is the maximum wavelength in meters (m),
- \(T\) is the absolute temperature of the blackbody in Kelvin (K),
- \(b\) is Wien's displacement constant, which is approximately \(2.897 \times 10^{-3} \text{ m} \cdot \text{K}\).
Given the temperature \(T = 100 \times 10^3 \text{ K}\), we can insert this value into the formula to calculate \(\lambda_{\text{max}}\).
By substituting into Wien's Displacement Law:
\[ \lambda_{\text{max}} = \frac{2.897 \times 10^{-3} \text{ m} \cdot \text{K}}{100 \times 10^3 \text{ K}} \]
Simplifying this gives:
\[ \lambda_{\text{max}} = \frac{2.897 \times 10^{-3}}{100 \times 10^3} \]
\[ \lambda_{\text{max}} = 2.897 \times 10^{-8} \text{ m} \]
Therefore, the maximum wavelength of a white dwarf with a temperature of \(100 \times 10^3\) K is \(2.897 \times 10^{-8} \text{ meters}\), which is in the ultraviolet part of the electromagnetic spectrum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fe8677b-d2b4-4cf1-b1ed-08820154fcb5%2F643705a1-742f-4841-8cfe-61be2f845eed%2Fdc1vwa_processed.png&w=3840&q=75)
Transcribed Image Text:**Question:**
White dwarfs have a temperature of \(100 \times 10^3\) K. Calculate the maximum wavelength of a white dwarf.
**Explanation:**
White dwarfs are a type of stellar remnant that are known for their high temperatures and typically exhibit temperatures in the range highlighted in the question. To determine the maximum wavelength (\(\lambda_{\text{max}}\)) emitted by a white dwarf, we can utilize Wien's Displacement Law. This law states:
\[ \lambda_{\text{max}} = \frac{b}{T} \]
where:
- \(\lambda_{\text{max}}\) is the maximum wavelength in meters (m),
- \(T\) is the absolute temperature of the blackbody in Kelvin (K),
- \(b\) is Wien's displacement constant, which is approximately \(2.897 \times 10^{-3} \text{ m} \cdot \text{K}\).
Given the temperature \(T = 100 \times 10^3 \text{ K}\), we can insert this value into the formula to calculate \(\lambda_{\text{max}}\).
By substituting into Wien's Displacement Law:
\[ \lambda_{\text{max}} = \frac{2.897 \times 10^{-3} \text{ m} \cdot \text{K}}{100 \times 10^3 \text{ K}} \]
Simplifying this gives:
\[ \lambda_{\text{max}} = \frac{2.897 \times 10^{-3}}{100 \times 10^3} \]
\[ \lambda_{\text{max}} = 2.897 \times 10^{-8} \text{ m} \]
Therefore, the maximum wavelength of a white dwarf with a temperature of \(100 \times 10^3\) K is \(2.897 \times 10^{-8} \text{ meters}\), which is in the ultraviolet part of the electromagnetic spectrum.
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