Atoms - Part 7 - Building Electronic Structure
The first quantum number determines the size, i.e., a 1s orbital is smaller than a 2s orbital which is smaller than a 3s orbital, etc. The energy of an orbital is determined mostly by the first two quantum numbers. The order in increasing energy is given below.
1s, 2s, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f ~ 5d, 6p, 7s, 5f ~ 6d
The table below gives the four quantum numbers up to the 3d orbitals.
| n | l | ml | ms | Name |
| 1 | 0 | 0 | ±½ | 1s |
| 2 | 0 | 0 | ±½ | 2s |
| 2 | 1 | -1 | ±½ | 2p |
| 0 | ±½ | |||
| 1 | ±½ | |||
| 3 | 0 | ±½ | 3s | |
| 3 | 1 | ±½ | 3p | |
| ±½ | ||||
| 3 | 2 | -2 | ±½ | 3d |
| -1 | ±½ | |||
| 0 | ±½ | |||
| 1 | ±½ | |||
| 2 | ±½ |
The Schrodinger equation cannot be solved exactly for atoms with two or more electrons. Yet with certain approximations the hydrogen-like orbitals apply to many electron atoms. When building the electronic configuration of many electron atoms we start by placing electrons in the lowest energy orbitals and work up from there. A key to the building of the electronic structure of many-electron atoms is the Pauli exclusion principle which states that no two electrons can have the same four quantum numbers.
For hydrogen the single electron goes into the 1s orbital.
The up-arrow indicates spin +½, the down-arrow spin -½.
For helium the two electrons, one of spin +½ and the other of spin -½, are placed in the 1s orbital.
The 1s orbital is filled with two electrons. With lithium the next electron goes into the orbital with the next highest energy, the 2s orbital.
With beryllium the 2s orbital is filled with two electrons.
With boron the next electron is placed in one of the 2p orbitals. The three 2p sublevels are all equivalent in energy.
The carbon atom has six electrons. The lowest energy is achieved by placing the next electron in one of the unoccupied 2p orbitals. Furthermore the lowest energy is achieved if both the 2p electrons have the same spin (parallel spin). Such electrons are called "unpaired".
When it comes to adding the second p orbital electron in the carbon atom there are three possibilities that follow the Pauli exclusion principle.
Hund's rule states that for any set of orbitals that are equal in energy the configuration with the maximum number of parallel spins results in the lowest electron-electron repulsion. This is the one to the left in the figure above.
For nitrogen, Hund's rule requires no paired electrons in the p subshells.
With oxygen there is an electron pair in one p orbital. The paired electrons are less tightly held than the unpaired electrons because of electron-electron repulsion. Thus the first ionization energy of oxygen is low. (The ionization energy is the energy required to remove an electron from an atom.)
Fluorine has one unpaired electron.
With neon the p orbitals are all filled with electron pairs. This is a very stable configuration with the completely filled shell. Neon is one of the noble gases.
Electronic structure through the filling of the 2p orbitals.
| At. No. | 1s | 2s | 2p | |
| 1 | H | 1 | ||
| 2 | He | 2 | ||
| 3 | Li | 2 | 1 | |
| 4 | Be | 2 | 2 | |
| 5 | B | 2 | 2 | 1 |
| 6 | C | 2 | 2 | 2 |
| 7 | N | 2 | 2 | 3 |
| 8 | O | 2 | 2 | 4 |
| 9 | F | 2 | 2 | 5 |
| 10 | Ne | 2 | 2 | 6 |
The first 10 elements in the form of the first two periods of the periodic table.
The first row (H, He) is called the first period and represents the filling of the 1s orbital. The second period (Li - Ne) represents the filling of the 2s and 2p orbitals.
The first ionization energies are high where an outer shell is filled such as with helium and neon.
Figure 19.
The upward trend from Li to Ne is due to the increasing nuclear charge.