Definition and explanation of spin quantum numbers
Spin Quantum Number:
Scientists Uhlenbeck and Goudsmit revealed that every electron, while revolving around the nucleus, continuously spins like a top around its own axis, either in a clockwise or a counter-clockwise direction. The quantum number that expresses the direction of an electron’s rotation around its own axis is called the Spin Quantum Number. It is generally denoted by s. The values of s are +1/2 and -1/2 (i.e., +1/2 and –1/2).
Due to these two types of rotation, it can have two values, namely +1/2 and -1/2. The energy of an electron also depends to some extent on the value of s. The general rule is that each orbital can accommodate two electrons with opposite spins (↑↓) in a state of mutual revolution. This is because, in this state, they experience a mutual magnetic attraction, making their paired state highly stable.
Key Characteristics and Importance:
- It provides a clear concept of the direction in which an electron in an atom is spinning relative to its own axis.
- It explains how two electrons can reside side-by-side simultaneously in a single orbital of an atom by pairing up.
- The scientific concept that electrons generate a magnetic field due to their spin within the atom is obtained from the spin quantum number.
- The overall magnetic properties (such as diamagnetic or paramagnetic behavior) of an atom can be comprehensively explained.
Note: Due to their rotation, electrons behave like tiny magnetic needles or bar magnets inside the atomic structure.
The total number of orbiters and electrons is determined by calculating the values of the four quantum numbers:-
| Principal Quantum Number (n) | Azimuthal Quantum Number (l) | Sub-shell | Magnetic Quantum Number (m) | Number of Orbitals | Spin Quantum Number (s) | Number of Electrons |
|---|---|---|---|---|---|---|
| 1 or K Shell | 0 | 1s | 0 | 1 | 1 (+12, –12) | 2 |
| 2 or L Shell | 0 | 2s | 0 | 1 | 1 (+12, –12) | 8 |
| 1 | 2p | +1, 0, -1 | 3 | 3 (+12, –12) | ||
| 3 or M Shell | 0 | 3s | 0 | 1 | 1 (+12, –12) | 18 |
| 1 | 3p | +1, 0, -1 | 3 | 3 (+12, –12) | ||
| 2 | 3d | +2, +1, 0, -1, -2 | 5 | 5 (+12, –12) | ||
| 4 or N Shell | 0 | 4s | 0 | 1 | 1 (+12, –12) | 32 |
| 1 | 4p | +1, 0, -1 | 3 | 3 (+12, –12) | ||
| 2 | 4d | +2, +1, 0, -1, -2 | 5 | 5 (+12, –12) | ||
| 3 | 4f | +3, +2, +1, 0, -1, -2, -3 | 7 | 7 (+12, –12) |
The total number of orbiters and electrons is determined by calculating the values of the four quantum numbers:-
| Principal Quantum Number (n) | Azimuthal Quantum Number (l) | Magnetic Quantum Number (m) | Number of Orbitals (2l + 1) |
Number of Electrons 2(2l + 1) |
|---|---|---|---|---|
| Value | Value | |||
| 1 or K Shell | 0 | 0 | 1 | 2 |
| 2 or L Shell | 0 | 0 | 1 | 2 |
| 1 | +1, 0, -1 | 3 | 6 | |
| 3 or M Shell | 0 | 0 | 1 | 2 |
| 1 | +1, 0, -1 | 3 | 6 | |
| 2 | +2, +1, 0, -1, -2 | 5 | 10 | |
| 4 or N Shell | 0 | 0 | 1 | 2 |
| 1 | +1, 0, -1 | 3 | 6 | |
| 2 | +2, +1, 0, -1, -2 | 5 | 10 | |
| 3 | +3, +2, +1, 0, -1, -2, -3 | 7 | 14 |
