To find the electron configuration for zinc, we need to understand that zinc has an atomic number of 30. This means zinc has 30 electrons. The electron configuration is determined by distributing these electrons into the various atomic orbitals following the Aufbau principle, Pauli exclusion principle, and Hund's rule.
The configuration progresses through filling up orbitals in the order of increasing energy levels. Here’s the step-by-step order in which the orbitals fill up:
1. 1s orbital can hold 2 electrons: [tex]\(1s^2\)[/tex]
2. 2s orbital can hold 2 electrons: [tex]\(2s^2\)[/tex]
3. 2p orbital can hold 6 electrons: [tex]\(2p^6\)[/tex]
4. 3s orbital can hold 2 electrons: [tex]\(3s^2\)[/tex]
5. 3p orbital can hold 6 electrons: [tex]\(3p^6\)[/tex]
6. 4s orbital can hold 2 electrons: [tex]\(4s^2\)[/tex]
7. 3d orbital can hold 10 electrons: [tex]\(3d^{10}\)[/tex]
Let's count the total number of electrons when we fill 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
- [tex]\(3p^6\)[/tex]: 6 electrons
- [tex]\(4s^2\)[/tex]: 2 electrons
- [tex]\(3d^{10}\)[/tex]: 10 electrons
Adding these up:
[tex]\(2 (1s) + 2 (2s) + 6 (2p) + 2 (3s) + 6 (3p) + 2 (4s) + 10 (3d) = 30\)[/tex] electrons
Therefore, the electron configuration for zinc (Zn) is:
[tex]\[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10}\][/tex]
Among the given options, the correct option is:
[tex]\[1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10}\][/tex]
This matches the fourth option.
