Sure, let's determine the correct electron configuration for titanium (Ti), which has an atomic number of 22.
This means titanium has 22 electrons. These electrons are arranged in atomic orbitals according to the Aufbau principle, Hund's rule, and the Pauli exclusion principle. The general order of filling is based on increasing energy levels:
1. Each orbital can hold a maximum of 2 electrons.
2. Electrons fill orbitals starting from the lowest energy level to the highest.
Following the order, we fill the orbitals as follows:
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 orbital 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 orbital can hold up to 6 electrons: [tex]\(3p^6\)[/tex]
6. 4s orbital is actually filled before the 3d orbital: [tex]\(4s^2\)[/tex]
7. 3d orbital can hold up to 10 electrons [tex]\(3d\)[/tex].
Counting the electrons added through each step, we get:
- [tex]\(1s^2\)[/tex] contributes 2 electrons.
- [tex]\(2s^2\)[/tex] contributes 2 electrons.
- [tex]\(2p^6\)[/tex] contributes 6 electrons.
- [tex]\(3s^2\)[/tex] contributes 2 electrons.
- [tex]\(3p^6\)[/tex] contributes 6 electrons.
- [tex]\(4s^2\)[/tex] contributes 2 electrons.
- Finally, adding 2 into the [tex]\(3d\)[/tex] orbital contributes 2 electrons.
Therefore, the total electron count is [tex]\(2 + 2 + 6 + 2 + 6 + 2 + 2 = 22\)[/tex] electrons, matching the atomic number 22.
So, the correct electron configuration for titanium (Ti) is:
[tex]\[
1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6 \ 4s^2 \ 3d^2
\][/tex]
Based on the choices provided:
1. [tex]\[1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6 \ 4s^2 \ 3d^2\][/tex]
2. [tex]\[1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6 \ 3d^4\][/tex]
3. [tex]\[1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6 \ 4s^2 \ 4p^2\][/tex]
The correct electron configuration for titanium (Ti) is [tex]\[1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6 \ 4s^2 \ 3d^2\][/tex].
Thus, the first option is the correct one.
