If a neutron star has a radius of 13 km and a temperature of 9.0 x 10° K, how luminous is it? Express your answer in watts and also in solar luminosity units. (Hint: Use the relation Use 5,800 K for the surface temperature of the Sun. The luminosity of the Sun is 3.83 x 1026 w.) luminosity in watts luminosity in solar luminosity units Le

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**Problem Statement:**

If a neutron star has a radius of 13 km and a temperature of \(9.0 \times 10^6 \, \text{K}\), how luminous is it? Express your answer in watts and also in solar luminosity units. 

**Hint:** Use the relation 

\[
\frac{L}{L_{\odot}} = \left( \frac{R}{R_{\odot}} \right)^2 \left( \frac{T}{T_{\odot}} \right)^4
\]

Use 5,800 K for the surface temperature of the Sun. The luminosity of the Sun is \(3.83 \times 10^{26} \, \text{W}\).

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**Required Calculations:**

- **Luminosity in watts:** [Input box]
- **Luminosity in solar luminosity units:** [Input box] \(L_{\odot}\)
Transcribed Image Text:**Problem Statement:** If a neutron star has a radius of 13 km and a temperature of \(9.0 \times 10^6 \, \text{K}\), how luminous is it? Express your answer in watts and also in solar luminosity units. **Hint:** Use the relation \[ \frac{L}{L_{\odot}} = \left( \frac{R}{R_{\odot}} \right)^2 \left( \frac{T}{T_{\odot}} \right)^4 \] Use 5,800 K for the surface temperature of the Sun. The luminosity of the Sun is \(3.83 \times 10^{26} \, \text{W}\). --- **Required Calculations:** - **Luminosity in watts:** [Input box] - **Luminosity in solar luminosity units:** [Input box] \(L_{\odot}\)
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