ATOMIC STRUCTURE MASTERY

Discoverer: J.J. Thomson (1897)

Charge: -1.602 × 10⁻¹⁹ C

Mass: 9.109 × 10⁻³¹ kg (1/1840 amu)

e/m ratio: 1.7588 × 10¹¹ C/kg

Properties: Wave-particle duality, quantized energy levels

Significance: First subatomic particle discovered

Discoverer: Eugene Goldstein (1886)

Charge: +1.602 × 10⁻¹⁹ C

Mass: 1.673 × 10⁻²⁷ kg (1.0073 amu)

e/m ratio: Variable (highest for H⁺)

Properties: Canal rays, nucleus constituent

Named by: Ernest Rutherford

Discoverer: James Chadwick (1932)

Charge: Neutral (0)

Mass: 1.675 × 10⁻²⁷ kg (1.0087 amu)

Experiment: α + ⁹Be → ¹²C + n

Properties: High penetration, nuclear stability

Significance: Explains isotopes

Particle	Symbol	Charge	Mass(amu)
Electron	e⁻	-1	0.0005486
Proton	p⁺	+1	1.0073
Neutron	n⁰	0	1.0087
Alpha	α²⁺	+2	4.0015

Note: Proton present in all atoms → common matter constituent

Key Postulate: Energy emitted/absorbed in discrete packets (quanta)

Energy of photon: E = hν = hc/λ = hcῡ

Planck’s constant: h = 6.626 × 10⁻³⁴ Js

Relationships:

• E ∝ ν (direct)

• E ∝ 1/λ (inverse)

• E ∝ ῡ (direct)

Significance: Foundation of quantum mechanics

Values: n = 1, 2, 3, 4… (K, L, M, N shells)

Determines:

• Shell/energy level

• Atomic radius (r ∝ n²)

• Energy (E ∝ 1/n² for H)

• Max electrons = 2n²

• Orbitals = n²

Periodic Table: Max n = Period number

Values: l = 0 to (n-1)

Subshells:

• l=0 → s (spherical)

• l=1 → p (dumbbell)

• l=2 → d (cloverleaf)

• l=3 → f (complex)

Determines:

• Orbital shape

• Angular momentum

• Orbitals = (2l+1)

Magnetic (m):

• Values: m = -l to +l

• Determines orbital orientation

• Example: p-orbitals: m=-1,0,+1 (px, py, pz)

Spin (s):

• Values: s = +½ (↑) or -½ (↓)

• Not from Schrödinger equation

• Introduced by Goudsmit & Uhlenbeck (1925)

• Determines electron spin direction

Formula: 1/λ = R (1/n₁² – 1/n₂²)

Rydberg constant: R = 1.097 × 10⁷ m⁻¹

n₁: Lower energy level

n₂: Higher energy level (n₂ > n₁)

Wave number: ῡ = 1/λ = R (1/n₁² – 1/n₂²)

Energy: ΔE = hc/λ = hcR (1/n₁² – 1/n₂²)

n₁ = 2, n₂ = 3,4,5…

Key Lines:

• Hα (red): 656.3 nm (3→2)

• Hβ (blue-green): 486.1 nm (4→2)

• Hγ (violet): 434.0 nm (5→2)

• Hδ (violet): 410.2 nm (6→2)

Region: Visible (380-750 nm)

Discovered: Johann Balmer (1885)

n₁ = 1, n₂ = 2,3,4…

Region: Ultraviolet (10-400 nm)

Highest energy series

Discovered: Theodore Lyman (1906)

Important lines:

• Ly-α: 121.6 nm (2→1)

• Ly-β: 102.6 nm (3→1)

• Ly-γ: 97.3 nm (4→1)

Paschen (n₁=3): IR, discovered 1908

Brackett (n₁=4): Far IR, discovered 1922

Pfund (n₁=5): Far IR, discovered 1924

Memory Aid:

“Lazy Bears Prefer Berries & Pineapples”

Lyman(1), Balmer(2), Paschen(3), Brackett(4), Pfund(5)

Longest λ: Pfund series

s-orbital: Spherical, 1 orientation

p-orbitals: Dumbbell, 3 orientations (px, py, pz)

d-orbitals: Cloverleaf (4), dz² different

f-orbitals: Complex, 7 orientations

Nodal surfaces:

• Radial nodes = n – l – 1

• Angular nodes = l

• Total nodes = n – 1

(n+l) Rule (Wiswesser):

Fill subshells in increasing (n+l) order

If equal (n+l), lower n first

Order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s...

Aufbau Principle:

Electrons occupy lowest energy orbitals first

Follows (n+l) order

Pauli Exclusion:

No two electrons can have identical quantum numbers

Max 2 electrons per orbital (opposite spins)

Hund’s Rule:

Electrons occupy degenerate orbitals singly before pairing

Maximizes parallel spins (minimizes repulsion)

Exceptions: Cr, Cu (half/full d-subshell stability)

Cr (Z=24): [Ar] 4s¹ 3d⁵ (not 4s² 3d⁴)

Cu (Z=29): [Ar] 4s¹ 3d¹⁰ (not 4s² 3d⁹)

Mo (Z=42): [Kr] 5s¹ 4d⁵ (similar to Cr)

Ag (Z=47): [Kr] 5s¹ 4d¹⁰ (similar to Cu)

Au (Z=79): [Xe] 6s¹ 4f¹⁴ 5d¹⁰

Reason: Extra stability of half/full subshells