## FSc Notes Chemistry Part 1 Chapter 5 Atomic Structure Lecture 6

### Quantum Numbers:

To give a comprehensive explanation of the structure of atom
according to modern concept, a set of four quantum numbers is presented. Three
of them are obtained from solution of wave theory and the fourth one shows the
spin of electrons in orbital.

These four quantum numbers are:

**Principle Quantum Number (n)****Azimuthal Quantum Number (l)****Magnetic Quantum Number (m)****Spin Quantum Number (ms)**

**1. Principle Quantum Number (n):**

**Principle quantum number gives us two information’s.**

**It tells us about the shell in which the electron under consideration is revolving.****It tells us about the no. of electrons in a particular shell, by the formula 2n2. Principle Q .No is denoted by "n" and the value of "n" and their related shell are as followed:**

N= 1,2,3,4,5,6,7 = K, L, M, N, O, P, Q

The maximum no. of electrons in a particular shell can be
calculated by the formula "2n2". Where "n" is principle
quantum number.

e.g

For "K" shell n=1

2(1)2 = 2 electrons

"L" shell n= 2 thus

2(2)2 = 8 electrons and so on.

**2. Azimuthal Quantum Number (l)**

**Azimuthal quantum number is also known as secondary cell. It is denoted by "l". The values of "l" are 0,1,2 & 3.**

The value of "l" can be determined by the formula
"n-1". Where "n" is Principle quantum number.

Azimuthal quantum number tells us about the sub—shells (orbits)
present in a particular shell.

It also explains the shape of an orbital.

If the value of l is "o", then it means
"s" sub—shell which is spherical.

When l=1 then it shows "P" sub—shell, whose shape
is dumbbell.

When l=2, then it shows "d" sub—shell, whose shape
is sausage.

When l=3 , then it shows "f" sub—shell, whose
shape is complicated.

**3. Magnetic Quantum Number (m):**

**Magnetic quantum number is denoted by "m" it is determined by the formula M= + l , 0 , -l**

**Where l= Azimuthal quantum number. Magnetic quantum number tell us about the no. of orbital’s ( sub—sub—shells ) in a particular sub—shell.**

For example.

K shell: n=1 , l=O , m=O

s orbit so s orbit has no orbitals. It is orbital itself.

**L Shell: n=2 , l=1 , m=+1, O , -1**

**p orbit has p orbit has 3 orbitals**

**d has five orbitals**

**f has seven orbitals**

**4. Spin Quantum Number: (s)**

**This quantum number is denoted by "ms". This quantum is number describes spin of an electron around its own axis. In an orbital the electron can spin either clockwise which is + 1/2 or anti—clock wise which is -1/2.**

If an orbit has two electrons with same spin, ie , this is
called parallel spin. When the two electrons in an orbital has opposite spin ie
. This is called anti—parallel or paired up spin. An orbital with only one
electron ie is known as half filled orbital.

### Electronic Configuration:

The process of filling of electrons in the orbitals of an
atom, is known as electronic

configuration.

During electronic configuration, the following three rules
are used.

#### 1. Pauli's Exclusion Principle:

In 1925, Wolfgang Pauli presented a principle, which can be
stated as:

**An orbital can have a maximum of two electrons and these electrons must have opposite spin ie or No two electrons in an orbital can have the same set of four quantum numbers"**#### 2. Hund's Rule:

**This rule states that if degenerate orbitals ( orbitals of same shape and energy ), then the electron will first till them singly with same spin and then will pair up. This rule is applicable in case of filling up of P, d and f orbits. For example if we want to place 3 electrons in P orbit then they are placed as:**

#### 3 Auf Bau Principle:

**This principle states that electron fill have orbitals in the increasing order of their energy. It means that first of all the electrons fill up that orbitals of lower energy and then fill up the orbitals of high energy. The increasing order of orbitals of an atom can be determined by "n + l" rule.**

N + L RULE:

N + L rule describes the increasing order of energy of
orbitals of an atom. Here "n" is principle quantum number while
"l" is azimuthal quantum number.

The main points of this rule are:

- orbit with lower n + l value will have lower energy.
- If two sub—shell have same n+l value, then the sub—shell with lower n+l value would have lower energy.So the increasing order of energy of orbitals is: 1S, 2S, 2P, 3S, 3P, 4S, and 4P…………………………..

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