The electronic configuration of calcium (Ca), which has an atomic number of 20, can be derived by filling the orbitals according to the Aufbau principle, while also applying Hund's rule where necessary.
Here’s how we can write the electronic configuration step by step for calcium:
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Identify the number of electrons: Calcium has 20 electrons.
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Fill the orbitals: Start filling the orbitals in the order of increasing energy levels, following the Aufbau principle (1s, 2s, 2p, 3s, 3p, 4s, etc.).
Using Hund's rule (which states that electrons will fill degenerate orbitals singly before pairing up), we still fill the orbitals one at a time as we go along.
The order of filling is:
- 1s: 2 electrons
- 2s: 2 electrons
- 2p: 6 electrons (filling each of the three p orbitals singly first, then pairing)
- 3s: 2 electrons
- 3p: 6 electrons (again, filling singly first, then pairing)
- 4s: 2 electrons (since 4s is lower in energy than 3d)
Putting this all together, the electronic configuration of calcium is:
\[ \text{Ca: } 1s^2 , 2s^2 , 2p^6 , 3s^2 , 3p^6 , 4s^2 \]
This can also be written in a shorthand notation using the electron configuration of the nearest noble gas (argon, Ar):
\[ \text{Ca: } [\text{Ar}] , 4s^2 \]
So, the final electronic configuration of calcium is either written completely as \(1s^2 , 2s^2 , 2p^6 , 3s^2 , 3p^6 , 4s^2\) or in shorthand as \([\text{Ar}] , 4s^2\).