To determine the electron configuration for germanium (Ge), which has an atomic number of 32, we must fill the electron orbitals following the Aufbau principle, which dictates the order in which orbitals are filled based on increasing energy levels. This principle is supplemented by Hund's rule and the Pauli exclusion principle.
Here are the step-by-step details for filling up the orbitals:
1. 1s orbital can hold up to 2 electrons.
[tex]$ 1s^2 $[/tex]
2. 2s orbital can hold up to 2 electrons.
[tex]$ 2s^2 $[/tex]
3. 2p orbitals (which has 3 sub-orbitals) can hold up to 6 electrons.
[tex]$ 2p^6 $[/tex]
4. 3s orbital can hold up to 2 electrons.
[tex]$ 3s^2 $[/tex]
5. 3p orbitals can hold up to 6 electrons.
[tex]$ 3p^6 $[/tex]
6. 4s orbital can hold up to 2 electrons.
[tex]$ 4s^2 $[/tex]
7. 3d orbitals (which has 5 sub-orbitals) can hold up to 10 electrons.
[tex]$ 3d^{10} $[/tex]
8. 4p orbitals can hold up to 6 electrons, but for germanium with atomic number 32, we only need 2 electrons to complete the required 32 electrons.
[tex]$ 4p^2 $[/tex]
Putting all these together, the full electron configuration for germanium (Ge) is:
[tex]$ 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^2 $[/tex]
So, the correct answer from the given options is:
B. 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^{10} 4p^2
