Quantum number : A quantum number is a vaue that is used when describing the energy levels available to atoms and molecules.
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 numbrer, m 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 n has the value 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)`
number of electrons `= 2n^(2)`
7. This Quantum number describes the size and energy of the orbit.
(b) Azimuthal Quantum Number :
1. This was propsed 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 and 3 respectively.
7. The 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.
`{:("Main level","Sub-levels","Sub sub-levels"),(1,s,1s),(2,s,2s),(,p,2p),(3,s,3s),(,p,3p),(,d,3d),(4,s,4s),(,p,4p),(,d,4d),(,f,4f):}`
8. The relative energy values of 1s, 2s, 2p etc., can be calculated by adding up their n and l 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.
`{:("Sub-level","Shape"),(s,"spherical"),(p,"dumb-bell"),(d,"double dumb-bell"),(f,"four-fold dumb-bell"):}`
(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 or orbitals present in a given sub-level.
4. .m. has values from -l to +l through .0.
5. The total number of .m. values for a given value of .l. is (2l + 1).
`{:("Sub-level","l value","m value","no. of orbitals"),(s,0,0,1),(p,1,"-1, 0, + 1",3),(d,2,"-2, -1, 0, +1, +2",5),(f,3,"-3, -2, -1, 0, + 1, + 2, + 3",7):}`
6. All the orbitals present in a given sub-level 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 `+ (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.
