How are the quantam numbers n, l and m arrived at ? Explain the significance of these quantam numbers.

Explanation

To describe an electron completely four quantum numbers were predicted .
They are
(1) Principal quantum number , n
(2) Azimuthal quantum number ,l
(3) Magnetic quantum number , `m_(1)` and
(4) Spin quantum number , `m_(s)`.
a) Principal Quantum Number:
1) This was proposed by Neils Bohr .
2) It is denoted by the letter 'n'.
3) It represents the circular orbits around the nucleus.
4) As the value of n increases the size and energy of the orbit increases.
5) According to number method a has the values 1 , 2 , 3 ..... According to letter method 'n' can be represented by the letters K , L , M , ..........
6 ) In any orbit , the number of sub-orbits = n number of orbitals = `n^(2)` ,
7 ) This Quantum number describes the size and energy of the orbit.
b) Azimuthal Quantum Number :
1 ) This was proposed by Sommerfeld .
2) It is also known as Angular momentum quantum number .
3) It is denoted by the letter 'l'.
4) This quantum number represents the sub-levels present in the main levels.
5 ) The sub-levels are s , p , d and f .
6) The l values of s , p , d and f sub-levels are 0 , 1 , 2 ans 3 respectively .
7) This first main level contains only one sub-level and it is s . The second main level contains s , p sub-levels . The third main level contains s, p , d sub-levels . The fourth main level contains s, p d and f sub-levels.

8) The relative values of 1s, 2s,2p etc . can be calculate by adding up their n and 1 values .
Ex :1 Energy value of 1s = 1 + 0 = 1
2. Energy value of 2p = 2 + 1 = 3

3. Energy value of 3d = 3 + 2 = 5
4. Energy value of 4f = 4+3 = 7
9) This Quantum number describes the shape of the orbital .

c) Magnetic Quantum Number :
1) This was proposed by Lande .
2) It is denoted by the letter 'm' .
3) This quantum number describes the sub-sub levels of orbitals present in a given sub-level.
4) `'m_(1)'` has values from -l to + l through '0'.
5) The total number of 'm' values for given value of 'l' (2l+1)
6) All the orbitals present in a given sublevel possesses the same energy values because they possess the same n and l values .
7) This quantum number describes the orientation of the orbitals in space .
d) Spin Quantum Number :
1) It was proposed by Uhlenbeck and Goudsmit.
2) It is denoted by `m_(s)` .
3) This quantum number describes the spin of the revolving electron .
4) `'m_(s)'` value of clockwise electron is `+1//2` and that of anticlockwise electron is `-1//2` .
5) Clockwise revolving electron is represented by `+1//2` and anticlockwise revolving electron is represented by `-1//2` .
6) This quantum number describes the direction of spin of the revolving electron.