If a neutron star has a radius of 9.12 km and a temperature of 3.63 x 106 K, how luminous is it in watts? w How does its luminosity compare to the Sun (3.83 x 1026 w)? Lsun
Stellar evolution
We may see thousands of stars in the dark sky. Our universe consists of billions of stars. Stars may appear tiny to us but they are huge balls of gasses. Sun is a star of average size. Some stars are even a thousand times larger than the sun. The stars do not exist forever they have a certain lifetime. The life span of the sun is about 10 billion years. The star undergoes various changes during its lifetime, this process is called stellar evolution. The structure of the sun-like star is shown below.
Red Shift
It is an astronomical phenomenon. In this phenomenon, increase in wavelength with corresponding decrease in photon energy and frequency of radiation of light. It is the displacement of spectrum of any kind of astronomical object to the longer wavelengths (red) side.
![**Problem Statement:**
If a neutron star has a radius of 9.12 km and a temperature of \(3.63 \times 10^6\) K, how luminous is it in watts?
- [Input Box] W
How does its luminosity compare to the Sun (\(3.83 \times 10^{26}\) W)?
\[
\frac{L_*}{L_{\text{Sun}}} =
\]
**Instructions:**
1. **Calculate Luminosity:**
- Use the formula for luminosity \(L = 4 \pi R^2 \sigma T^4\), where \(R\) is the radius, \(\sigma\) is the Stefan-Boltzmann constant, and \(T\) is the temperature.
- Substitute the given values to find the luminosity in watts.
2. **Compare Luminosity to the Sun:**
- Divide the calculated luminosity of the neutron star by the Sun’s luminosity to find the ratio \(\frac{L_*}{L_{\text{Sun}}}\).
**Note:**
This section allows learners to understand the basic concepts of stellar luminosity and perform calculations comparing different stellar objects.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F00bcc8d6-6f95-4e12-a823-a4a3b5b387f2%2F3089d71b-236f-411d-b1d3-7a375736485a%2F653r9pi_processed.png&w=3840&q=75)
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