To complete the electron configuration of a calcium atom, we need to distribute its electrons into the appropriate orbitals following the principles of quantum mechanics, especially the Aufbau principle, Pauli exclusion principle, and Hund’s rule. Calcium has an atomic number of 20, meaning it possesses 20 electrons that need to be placed into orbitals. Here’s the step-by-step distribution:
1. 1s orbital: The 1s orbital can hold a maximum of 2 electrons.
[tex]\[
1s^2
\][/tex]
2. 2s orbital: The 2s orbital can also hold up to 2 electrons.
[tex]\[
2s^2
\][/tex]
3. 2p orbital: The 2p sublevel can hold a total of 6 electrons, as it has three degenerate p orbitals.
[tex]\[
2p^6
\][/tex]
4. 3s orbital: The 3s orbital can hold up to 2 electrons.
[tex]\[
3s^2
\][/tex]
5. 3p orbital: The 3p sublevel, like the 2p sublevel, can hold 6 electrons.
[tex]\[
3p^6
\][/tex]
6. 4s orbital: The 4s orbital is next in line to be filled after the 3p, according to the Aufbau principle. It holds 2 electrons.
[tex]\[
4s^2
\][/tex]
Combining all of these steps, we get the complete electron configuration of a calcium atom:
[tex]\[
\text{Ca: } 1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6 \ 4s^2
\][/tex]
Thus, the full electron configuration for a calcium atom is:
[tex]\[
1s^2 \ 2s^2 \ 2p^6 \ 3s^2 \ 3p^6 \ 4s^2
\][/tex]
