## 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,

**which is equal to**

*l***, thus**

*n -1***can have one value (=0) and**

*l***can also have one value (=0). Hence,**

*m***can be either +1/2 or -1/2. There can be two possibilities for**

*s***= 1**

*n*= 1;*n*= 0;*l*= 0;*m*= +1/2*s*= 1;*n*= 0;*l*= 0;*m*= -1/2*s*

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,

**can have two values (= 0 and 1 which corresponds to s and p sub shells respectively),**

*l***will have three values (=-1, 0, +1) which corresponds to three orbitals of p sub shell and**

*m***can have two values +1/2 or -1/2. From this information, following combination will be obtained:**

*s*= 2;*n*= 0;*l*= 0;*m*= +1/2*s*= 2;*n*= 0;*l*= 0;*m*= -1/2*s*

= 2;*n*= 1;*l*= -1;*m*= +1/2*s*

= 2;*n*= 1;*l*= 0;*m*= +1/2*s*= 2;*n*= 1;*l*=+1;*m*= +1/2*s*= 2;*n*= 1;*l*= -1;*m*= -1/2*s*

= 2;*n*= 1;*l*= 0;*m*= -1/2*s*= 2;*n*= 1;*l*=+1;*m*= -1/2*s*

Therefore, L orbit where ** n** = 2 can accommodate total of

**electrons,**

*eight***in s sub shell and**

*two***in p sub shell. Likewise, the M orbit with**

*six***= 3 can accommodate**

*n***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.

**Remember:**

- The maximum number of electrons in any orbit or shell is 2
*n*^{2}, whereis a principal quantum number or the number of the orbit.*n* - 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
**(**is minimum. When*n + l)*has the same value for two or more orbitals, the new electron enters the orbital where*(n + l)*is minimum. This was given as*n***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:

*For NCERT Solutions for Class 11 Chemistry – Electrons in Orbitals are available, for details click CBSE Class 11 Chemistry***. **

- 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**

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