Quantum Numbers
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Topic Summary & Highlights
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Core Concept
Quantum numbers are sets of numerical values that describe the position, energy, and spin of an electron in an atom. They define the electron's orbital and distinguish one electron from another within an atom.
Practice Tips
Quantum numbers describe the location, energy, and spin of electrons in atoms.
The combination of n,l,ml,n, l, m_l,n,l,ml, and msm_sms defines a specific electron.
Understanding quantum numbers is critical for explaining atomic structure, periodic trends, and chemical behavior.
The Four Quantum Numbers
| Quantum Number | Symbol | Description | Possible Values |
|---|---|---|---|
| Principal Quantum Number | n | Energy level and size of the orbital | 1, 2, 3, ... |
| Angular Momentum Quantum Number | l | Shape of the orbital (subshell) | 0 to n-1 |
| Magnetic Quantum Number | ml | Orientation of the orbital in space | -l to +l |
| Spin Quantum Number | ms | Spin direction of the electron | +1/2, -1/2 |
Principal Quantum Number (n):
Definition: Determines the energy level and size of the orbital.
Values: Positive integers (n = 1, 2, 3, ,…).
Key Points:
Higher n: Larger orbital and higher energy.
Example: Electrons in n = 1 are closer to the nucleus than those in n=2.
Angular Momentum Quantum Number (l):
Definition: Determines the shape of the orbital (subshell).
Values: Integers from 0 to n−1.
Subshell Designations:
l=0: s-orbital (spherical).
l=1: p-orbital (dumbbell-shaped).
l=2: d-orbital (cloverleaf-shaped).
l=3: f-orbital (complex shapes).
Key Points:
For n=3, l = 0, 1, 2, corresponding to 3s,3p,3d.
Magnetic Quantum Number ($m_l$):
Definition: Determines the orientation of the orbital in space.
Values: Integers from −l to +l, including 0.
Example: For l=1 (p-orbital), m_l = -1, 0, +1, representing px,py,pzp_x, p_y, p_zpx,py,pz.
Spin Quantum Number ($m_s$):
Definition: Describes the spin direction of an electron.
Values: +12+\frac{1}{2}+21 (spin-up) or −12-\frac{1}{2}−21 (spin-down).
Key Points:
Each orbital can hold a maximum of 2 electrons, with opposite spins.
