6. examine the number of electrons in the energy levels for each atom. describe how they are related to the number of protons.

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# Brief Explanations:
1. **Electron Configuration Basics**: In a neutral atom, the number of electrons equals the number of protons (atomic number, $Z$). Electrons fill energy levels (shells) following the Aufbau principle, Pauli exclusion principle, and Hund's rule. The maximum number of electrons in a shell $n$ is $2n^2$ (e.g., $n = 1$ holds 2, $n = 2$ holds 8, $n = 3$ holds 18, etc.).
2. **Helium (He, $Z = 2$)**:
   - Energy level 1 ($n = 1$): Follows $2(1)^2 = 2$ electrons. Since He is neutral, electrons = protons = 2, so all 2 electrons occupy the first shell.
3. **Oxygen (O, $Z = 8$)**:
   - Energy level 1 ($n = 1$): Fills with 2 electrons (max for $n = 1$).
   - Energy level 2 ($n = 2$): Remaining electrons: $8 - 2 = 6$. The max for $n = 2$ is $2(2)^2 = 8$, so 6 electrons occupy the second shell.
4. **Sodium (Na, $Z = 11$)**:
   - Energy level 1 ($n = 1$): 2 electrons.
   - Energy level 2 ($n = 2$): $2(2)^2 = 8$ electrons (fills this shell).
   - Energy level 3 ($n = 3$): Remaining electrons: $11 - (2 + 8) = 1$, so 1 electron in the third shell.
5. **Relation to Protons**: In neutral atoms, total electrons (sum of electrons in all energy levels) equal the number of protons (atomic number). This ensures electrical neutrality (protons’ positive charge balances electrons’ negative charge).

# Answer:
- **Helium (He, $Z = 2$)**: Energy level 1 ($n = 1$) has 2 electrons (matches $2n^2$ for $n = 1$). Total electrons = 2 (equal to protons, $Z = 2$).
- **Oxygen (O, $Z = 8$)**: Energy level 1: 2 electrons; Energy level 2: 6 electrons. Total electrons = $2 + 6 = 8$ (equal to protons, $Z = 8$).
- **Sodium (Na, $Z = 11$)**: Energy level 1: 2; Energy level 2: 8; Energy level 3: 1. Total electrons = $2 + 8 + 1 = 11$ (equal to protons, $Z = 11$).

In neutral atoms, the **total number of electrons (sum of electrons in all energy levels)** equals the **number of protons (atomic number)** to maintain electrical neutrality.

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