Organic Chemistry/Foundational concepts of organic chemistry/Atomic structure/Filling electron shells

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When an atom or ion receives electrons into its orbitals, the orbitals and shells fill up in a particular manner.

There are three principles that govern this process: 1) the Aufbau (build-up) principle, 2) the Pauli exclusion principle, and 3) Hund's rule.

Exclusion principle

No more than one electron can have all four quantum numbers the same. What this translates to in terms of our pictures of orbitals is that each orbital can only hold two electrons, one "spin up" and one "spin down".

Build-up principle

You may consider an atom as being "built up" from a naked nucleus by gradually adding to it one electron after another, until all the electrons it will hold have been added. Much as one fills up a container with liquid from the bottom up, so also are the orbitals of an atom filled from the lowest energy orbitals to the highest energy orbitals.

However, the three p orbitals of a given shell all occur at the same energy level. So, how are they filled up? Is one of them filled full with the two electrons it can hold first? Or do each of the three orbitals receive one electron apiece before the any single orbital is double occupied. As it turns out, the latter situation occurs.

Hund's rule

This rule is applicable only for those elements that have d electrons, and so is less important in organic chemistry (though it is important in organometallic chemistry). It says that filled and half-filled shells tend to have additional stability. In some instances, then, for example, the 4s orbitals will be filled before the 3d orbitals.

Building atoms with quantum mechanics (advanced topic)

The equations (like the Legendre polynomials that describe spherical harmonics, and thus the shapes of orbitals) of quantum mechanics are distinguished by four types of numbers. The first of these quantum numbers is referred to as the principal quantum number, and is indicated by n. This merely represents which shell electrons occupy, and shows up in the periodic chart as the rows of the periodic chart. It has integral values, n=1,2,3 . . . . The highest energy electrons of the atoms in the first row all have n=1. Those in the atoms in the second row all have n=2. As one gets into n=3, Hund's rule mixes it up a little bit, but when one gets to the end of the third row, at least, the electrons with the highest energy have n=3.

The next quantum number is indicated by the letter m and indicates how many different types of shells an atom can have. Those elements in the first row can have just one, the s orbital. The elements in the second row can have two, the s and the p orbitals. The elements in the third row can have three, the s, p, and d orbitals. And so on. It may be funny to think of s, p and d as "numbers", but these are used as an historical and geometrical convenience.

The third kind of quantum number m_l specifies, for those kinds of orbitals that can have different shapes, which of the possible shapes one is referring to. So, for example, a 2p_z orbital indicates three quantum numbers, represented respectively by the 2, the p and the z.

Finally, the fourth quantum number is the spin of the electron. It has only two possible values, +1/2 or -1/2.

Pretty much only computational chemists have to treat quantum numbers as numbers per se is equations. But it helps to know that the wide variety of elements of the periodic table and the different shapes and other properties of electron orbitals have a unifying principle--the proliferation of different shapes is not completely arbitrary, but is instead bounded by very specific rules. Afbau Principle (it means 'building up'):- It states that the orbitals should be filled according to their increasing energies Thus the lowest energy orbital which is available is filled first. The increasing order of energies of the various orbitals is:-

1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p,6s,4f,5d,6p,7s,5f......

The order of increasing of energy of orbitals can be calc. from(n+l) rule or 'Bohr bury rule' According to this rule, the value of n+l is the energy of the orbital and such on orbital will be filled up first. e.g. 4s orbital having lower value of(n+l) has lower energy than 3d orbital and hence 4s orbital is filled up first. For 4s orbital, n+l=4+0=4 For 3d orbital, n+l=3+2=5,therefore 4s orbital will be filled first.