## Structure of Atom

# Quantum Numbers and Electronic Configuration of Elements

**Quantum Numbers :**

- a. Principal quantum number (n)
- b. Azimuthal quantum number (l)
- c. Magnetic quantum number (m)
- d. Spin quantum number (s)

**a. Principal quantum number (n)**

r_{n} = 0.54\frac{n^{2}}{Z}

Indicates size of the orbit.

Indicates energy of electron

**b. Azimuthal quantum number (l)**

Denoted by letter ' l ' and can have value from 0,1 to (n − 1)

l = 0 → s orbital → spherical

l = 1 → p orbital → dumb-bell

l = 2 → d orbital → double dumb-bell

l = 3 → f orbital → fore fold

**c. Magnetic quantum number (m)**

can have values −l to +l

total values (2l + 1)

**d. Spin quantum number (s)**

It can have values s = +½ and s = −½

**Exchange Energy :**

Exchange Energy = ^{n}C_{2}

=\frac{n!}{(n - 2)! \ 2!}

n = no.of unpaired electrons

Cr = 3d^{5} 4s^{1}

n = 6 ^{6}C_{2} = 15

Magnetic \ moment (\mu) = \sqrt{n(n + 2)} BM

n | μ=\sqrt{n(n + 2)} BM |

1 | \sqrt{3}=1.732 BM |

2 | \sqrt{8}=2.823 BM |

3 | \sqrt{15}=3.89 BM |

4 | \sqrt{24}=4.88 BM |

5 | \sqrt{35}=5.89 BM |

**Electronic configuration :**

nl^{x} method

moeller diagram :

1s < 2s < 2p <3s <3p < 4s < 3d < 4p < 3s < 4d < 5p < 6s < 4f < < 5d < 6p < 7s < 5f < 6d < 7p < 8s

### Part1: View the Topic in this Video from 37:35 to 50:55

### Part2: View the Topic in this Video from 1:17 to 18:35

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1. The number of electrons in subshell = 2(2*l* + 1).

2. Number of orbitals in main energy level = n^{2}.

3. Maximum number of electrons in *n*th shell = 2n^{2}4. The orbital angular momentum of an electron = \tt \sqrt{l\left(l + 1\right)}\frac{h}{2\pi}

5. Spin angular momentum = \tt \sqrt{s\left(s + 1\right)}\frac{h}{2\pi}

6. Magnetic moment = \tt \sqrt{n\left(n + 2\right)} B.M. (Bohr magneton) of n unpaired e^{-}