Chemistry Unit: 2 RULES FOR FILLING ELECTRONS IN ORBITALS
Chemistry notes for class 11: The four quantum numbers; principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m) and spin quantum number (s), define completely the position of an electron in an atom. They define the position of an electron in the major energy level (n), sub-energy level (l), orientation in sub-energy level (m), and the direction of the spin (s). Therefore, simply by stating the four quantum numbers, it is possible to identify an electron in an atom completely. This is because no two electrons in the same atom can have the same four quantum numbers. This fact is based on the Pauli Exclusion Principle which was given by an Austrian Physicist, Wolfgang Pauli. According to this principle, it is impossible for any two electrons in the same atom to have all the four quantum numbers the same.
This principle is very important in determining the maximum number of electrons that can exist in any quantum group i.e. shells and subshells. For K orbit, n = 1. So, l which is equal to n -1, thus l can have one value (=0) and m can also have one value (=0). Hence, s can be either +1/2 or -1/2. There can be two possibilities for n= 1
- n= 1; l = 0; m = 0; s = +1/2
- n = 1; l = 0; m = 0; s = -1/2
This means, that in K orbit, there is only one subshell i.e. l = 0 which is s- subshell which has one orbital. In this, only two electrons of opposite spins can be accommodated.
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For L- orbit, n = 2, l can have two values (= 0 and 1 which corresponds to s and p sub shells respectively), m will have three values (=-1, 0, +1) which corresponds to three orbitals of p sub shell and s can have two values +1/2 or -1/2. From this information, following combination will be obtained:
- n = 2; l = 0; m = 0; s = +1/2
- n = 2; l = 0; m = 0; s = -1/2
- n = 2; l = 1; m = -1; s = +1/2
- n = 2; l = 1; m = 0; s = +1/2
- n = 2; l = 1; m =+1; s = +1/2
- n = 2; l = 1; m = -1; s = -1/2
- n = 2; l = 1; m = 0; s = -1/2
- n = 2; l = 1; m =+1; s = -1/2
Therefore, L orbit where n = 2 can accommodate total of eight electrons, two in s sub shell and six in p sub shell. Likewise, the M orbit with n = 3 can accommodate 18 electrons; 2 in s sub shell (l = 0), 6 in p sub shell (l= 1) and 10 in d sub shell (l= 2).
As we pass from one element to another (one of next higher atomic number), one electron is added every time to the atom.
- The maximum number of electrons in any orbit or shell is 2n2, where n is a principal quantum number or the number of the orbit.
- The maximum number of electrons in a subshell (s, p, d or f) is equal to 2(2l + 1), where l is an azimuthal quantum number) and has the value 0, 1, 2 or 3. Thus, these subshells can have a maximum of 2, 6, 10 and 14 electrons respectively.
- Orbitals are filled up in order of their increasing energy. The orbital with lower energy is filled up first, then the orbital with higher energy starts filling up. A new electron enters the orbital where (n + l) is minimum. When (n + l) has the same value for two or more orbitals, the new electron enters the orbital where n is minimum. This was given as Aufbau Principle. According to this principle, the electrons are first accommodated in the orbitals of lowest energy. The sequence of filling of electrons according to Aufbau principle is obtained which is given below:
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- There can be one s-orbital, three p- orbitals, five d-orbitals and seven f- orbitals. Each one of these orbitals can hold only two electrons with spins of +1/2 and -1/2.
- Electron pairing in any s, p, d or f orbitals is not possible until all available orbitals of a given set contain one electron each. This is known as Hund’s rule of maximum multiplicity.
- Electrons tend to enter those subshells which, in a way, get either completely filled or exactly half-filled
Summary of electron filling rules