To find the ground-state electron configuration of magnesium (Mg), which has an atomic number of 12, we follow the order in which atomic orbitals are filled according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle.
1. Identify the Atomic Number: Magnesium has an atomic number of 12, which means it has 12 electrons.
2. Order of Filling Electron Orbitals: Electrons fill atomic orbitals in the following order based on increasing energy levels:
- 1s
- 2s
- 2p
- 3s
- 3p
- 4s
- 3d
- 4p
- ...
3. Fill the Orbitals:
- The 1s orbital can hold 2 electrons: [tex]\( 1s^2 \)[/tex].
- The 2s orbital can hold 2 electrons: [tex]\( 2s^2 \)[/tex].
- The 2p orbital can hold 6 electrons: [tex]\( 2p^6 \)[/tex].
- The 3s orbital can hold 2 electrons: [tex]\( 3s^2 \)[/tex].
So, distributing the 12 electrons in these orbitals:
- [tex]\( 1s^2 \)[/tex] (2 electrons)
- [tex]\( 2s^2 \)[/tex] (2 electrons)
- [tex]\( 2p^6 \)[/tex] (6 electrons)
- [tex]\( 3s^2 \)[/tex] (2 electrons)
4. Write the Configuration: Combining all the filled orbitals, the electron configuration is:
[tex]\[ \text{Mg: } 1s^2 2s^2 2p^6 3s^2 \][/tex]
Thus, the ground-state electron configuration for magnesium is:
[tex]\[ 1s^2 2s^2 2p^6 3s^2 \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{1s^2 2s^2 2p^6 3s^2} \][/tex]
