Use the Saha equation to determine the fraction of Hydrogen atoms that are ionized NI/Ntotal at the center of the Sun, where the temperature is 15.7 million K and the electron number density is ne=6.1x1031 /m³. Don't try to compare your result with actual data, as your result will be lower due to not taking the pressure into account. Since most of the neutral H atoms are in the ground state, use Zdegeneracy=2 and, since a H ion is just a proton, Zi=1. Also, use Xi=13.6 eV.

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### Using the Saha Equation to Determine Ionization in the Sun's Core

The task is to determine the fraction of hydrogen atoms at the center of the Sun that are ionized, denoted as \(N_{II}/N_{\text{total}}\). The parameters provided for this calculation are as follows:

- **Temperature**: 15.7 million Kelvin (K)
- **Electron number density**: \(n_e = 6.1 \times 10^{31} \, /\text{m}^3\)

**Important Notes**:

- The result might be lower than real conditions because the calculation doesn't consider pressure.
- Assume most neutral hydrogen (H) atoms are in the ground state. Thus, the degeneracy factor \(Z_I \approx 2\).
- Since a hydrogen ion is merely a proton, \(Z_{II} = 1\).
- The ionization potential \( \chi_I \) is 13.6 electron volts (eV).

This calculation will provide an approximation of the ionization fraction using the Saha equation, which is a critical concept in understanding stellar atmospheres and the physical conditions in the Sun’s core.
Transcribed Image Text:### Using the Saha Equation to Determine Ionization in the Sun's Core The task is to determine the fraction of hydrogen atoms at the center of the Sun that are ionized, denoted as \(N_{II}/N_{\text{total}}\). The parameters provided for this calculation are as follows: - **Temperature**: 15.7 million Kelvin (K) - **Electron number density**: \(n_e = 6.1 \times 10^{31} \, /\text{m}^3\) **Important Notes**: - The result might be lower than real conditions because the calculation doesn't consider pressure. - Assume most neutral hydrogen (H) atoms are in the ground state. Thus, the degeneracy factor \(Z_I \approx 2\). - Since a hydrogen ion is merely a proton, \(Z_{II} = 1\). - The ionization potential \( \chi_I \) is 13.6 electron volts (eV). This calculation will provide an approximation of the ionization fraction using the Saha equation, which is a critical concept in understanding stellar atmospheres and the physical conditions in the Sun’s core.
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