Quantum Numbers | Structure of Atom Class 11 Notes

Quantum Numbers

Complete Guide to Electronic Configuration | Class 11 Chemistry

1. Introduction

Quantum Numbers are a set of four numbers used to describe the position, energy, and spin of an electron in an atom. They serve as the "address" of an electron.

2. Principal Quantum Number ($n$)

• Significance: Determines the main energy shell and size of the orbital.
• Values: $n = 1, 2, 3, 4, ...$ (K, L, M, N shells).
• Max Electrons: The maximum number of electrons in a shell is $2n^2$.

3. Azimuthal Quantum Number ($l$)

• Also known as: Angular Momentum or Subsidiary Quantum Number.
• Significance: Determines the shape of the orbital (subshell).
• Values: $0$ to $n-1$.

Values for subshells:

• $l = 0 \rightarrow s$ (Spherical)
• $l = 1 \rightarrow p$ (Dumbbell)
• $l = 2 \rightarrow d$ (Double Dumbbell)
• $l = 3 \rightarrow f$ (Complex)

$$ \text{Orbital Angular Momentum} = \sqrt{l(l+1)} \frac{h}{2\pi} $$

4. Magnetic Quantum Number ($m_l$)

• Significance: Determines the spatial orientation of the orbital relative to a standard coordinate system.
• Values: Integers from $-l$ to $+l$ (including 0).
• Total Orbitals: Number of orbitals in a subshell = $2l + 1$.

Example: For $p$-subshell ($l=1$), $m = -1, 0, +1$ (3 orbitals: $p_x, p_y, p_z$).

5. Spin Quantum Number ($m_s$)

• Significance: Describes the direction of electron spin on its own axis.
• Values: $+1/2$ (Clockwise/Up) or $-1/2$ (Anti-clockwise/Down).
• Note: This number is not derived from the Schrödinger wave equation.

6. Summary Table

Shell (n)	Subshell (l)	Notation	No. of Orbitals ($2l+1$)	Max Electrons
1	0	1s	1	2
2	0, 1	2s, 2p	1, 3	2 + 6 = 8
3	0, 1, 2	3s, 3p, 3d	1, 3, 5	2 + 6 + 10 = 18
4	0, 1, 2, 3	4s, 4p, 4d, 4f	1, 3, 5, 7	2 + 6 + 10 + 14 = 32

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