Structure of Atom

Dalton once said atoms are indivisible — like unbreakable laddoos. But later experiments showed atoms themselves are made of even smaller particles.

Electron discovered by J.J. Thomson in 1897 using a cathode ray tube. When high voltage is applied, a stream of negatively charged particles comes out from the cathode — called cathode rays. They travel straight, cause fluorescence where they hit, and bend in electric and magnetic fields. Thomson measured their charge-to-mass ratio (e/m). Electron charge is -1.602 × 10⁻¹⁹ C, mass is 9.1 × 10⁻³¹ kg — almost negligible, about 1/1837 of a proton.

Proton discovered by E. Goldstein in 1886 as anode rays or canal rays. While cathode rays come from cathode, anode rays come from anode side — they are positive. Proton charge is +1.602 × 10⁻¹⁹ C, mass is 1.0073 amu, about 1836 times heavier than electron (1.67 × 10⁻²⁷ kg).

Neutron discovered by James Chadwick in 1932 by bombarding beryllium with alpha particles (Be + α → C + n). It has no charge — neutral — and mass is 1.0087 amu, slightly more than proton. So atom is: nucleus contains protons + neutrons, electrons revolve outside in extra-nuclear space.

Thomson plum pudding model 1898: He imagined atom as a sphere of uniformly spread positive charge with electrons embedded in it like seeds in a watermelon or raisins in a Christmas pudding. It explained neutrality, but it could not explain the results of alpha-ray scattering.

Rutherford nuclear model 1911 — Gold foil experiment: Rutherford bombarded a very thin gold foil with high-speed alpha particles. He observed: most alphas passed straight through, a few deflected by small angles, and very few (1 in 20,000) bounced back at 180°. Conclusion: Atom is mostly empty space, all positive charge and most mass is concentrated in a tiny central core called nucleus. Size of nucleus ~10⁻¹⁵ m while atom ~10⁻¹⁰ m — nucleus is 1,00,000 times smaller, like a pea in a football stadium. Electrons revolve around nucleus. Drawback: According to classical physics, revolving electron would continuously lose energy and fall into nucleus — atom would be unstable. Also it could not explain line spectrum.

Bohr model 1913: Bohr fixed this. He said electrons revolve only in certain fixed circular orbits with quantized angular momentum mvr = nh/2π. Energy and radius are quantized: rₙ = 0.529 × n²/Z Å and Eₙ = -13.6 × Z²/n² eV. When electron jumps from higher to lower orbit, it emits photon with ΔE = hν. This beautifully explains hydrogen spectrum — Lyman (UV), Balmer (visible), Paschen, Brackett, Pfund series. Limitations: Works only for single-electron species (H, He⁺, Li²⁺), fails for multi-electron atoms, cannot explain Zeeman effect (splitting in magnetic field) and doesn't include wave nature of electron.

Quantum numbers are like the full postal address of an electron — they tell us where it lives in the atom.

Principal quantum number n = 1,2,3... Tells size and energy of shell. Larger n means larger size and higher energy. n=1 is K shell, n=2 L, n=3 M, n=4 N — like floors of a building, higher floor more energy needed to reach.

Azimuthal quantum number l = 0 to (n-1) Tells shape of subshell. l=0 is s orbital — spherical like a football. l=1 is p — dumbbell shape. l=2 is d — double dumbbell/clover shape. l=3 is f — complex flower shape. For n=1, l can only be 0 (only 1s). For n=2, l=0,1 (2s,2p). For n=3, l=0,1,2 (3s,3p,3d).

Magnetic quantum number m = -l to +l Tells orientation in space. For l=0, m=0 — one orbital (s). For l=1, m=-1,0,+1 — three p orbitals (px, py, pz). For l=2, m has 5 values — five d orbitals. For l=3, seven f orbitals. Total orbitals in a shell = n².

Spin quantum number s = +½ or -½ Tells spin of electron — clockwise (↑) and anticlockwise (↓). Two electrons in same orbital must have opposite spins.

We thought electron is a particle, but it also behaves like a wave — dual nature.

de Broglie 1924: He said every moving particle has a wave nature. Wavelength λ = h/mv = h/p, where h is Planck constant 6.626×10⁻³⁴ J·s, m is mass, v is velocity, p is momentum. For big objects like a cricket ball, λ is negligible, but for electron it's significant. This was proved by Davisson and Germer in 1927 — they showed electron beam diffracts like light, making rings on screen.

Heisenberg Uncertainty Principle 1927: It is impossible to measure exact position and exact momentum of a small particle like electron simultaneously. If you try to know position accurately, momentum becomes uncertain, and vice versa. Mathematically Δx × Δp ≥ h/4π or Δx × Δv ≥ h/4πm. Where Δx is uncertainty in position, Δp in momentum. This is why Bohr's fixed orbits fail — we cannot know exact path, we can only talk about probability of finding electron — electron cloud or orbital, not fixed orbit.

Schrodinger in 1926 gave the wave equation for electron: Ĥψ = Eψ, where Ĥ is Hamiltonian operator (total energy), ψ (psi) is wave function — amplitude of electron wave, E is energy. The important thing is ψ² — square of wave function gives probability of finding electron at a point — electron cloud picture.

Nodes: Places where probability is zero (ψ²=0). Two types: Radial (spherical) nodes = n-l-1 and Angular (planar) nodes = l. Total nodes = n-1. Example: 1s has 0 radial, 0 angular. 2s has 1 radial (n-l-1=1), 0 angular. 2p has 0 radial, 1 angular.

Shapes of orbitals: s orbital is spherical — 1s small sphere, 2s bigger sphere with one radial node inside. p orbitals are dumbbell — two lobes with nucleus in between. Three types: px along x, py along y, pz along z. d orbitals are double dumbbell — 5 types: dz² (doughnut with two lobes), dx²-y², dxy, dyz, dxz. f orbitals are complex with 7 orientations.

How do electrons fill orbitals? Three rules control admission like college admission rules.

Aufbau Principle (building up): Electrons fill lowest energy orbital first. Energy decided by (n+l) rule — lower (n+l) means lower energy. If two have same (n+l), lower n fills first. Order: 1s (1+0=1), 2s (2+0=2), 2p (2+1=3), 3s (3+0=3 but n=3 >2 so after 2p), 3p (4), 4s (4), 3d (5), 4p (5), 5s (5), 4d (6), 5p (6), 6s (6), 4f (7), 5d (7)... So sequence is 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f 5d 6p 7s 5f...

Pauli Exclusion Principle: No two electrons in same atom can have same set of 4 quantum numbers. So one orbital can hold max 2 electrons with opposite spins (↑↓). If spins same, they cannot be in same orbital.

Hund's Rule of Maximum Multiplicity: For equal energy orbitals (like p³ or d⁵), electrons first singly occupy each orbital with parallel spins (all ↑), then pairing starts. This gives maximum unpaired electrons and more stability. Example p² configuration is ↑ ↑ _ not ↑↓ _. p³ is ↑ ↑ ↑.

Electronic Configuration: Write as 1s² 2s² 2p⁶ etc. s can have max 2, p max 6, d max 10, f max 14. Using noble gas shorthand: Sodium 11 = [Ne]3s¹. Exceptions due to extra stability of half-filled and fully filled: Chromium 24 is [Ar]4s¹3d⁵ (not 4s²3d⁴) and Copper 29 is [Ar]4s¹3d¹⁰ (not 4s²3d⁹). Similarly Mo, Ag, Au show same. Reason: half-filled and fully filled have more symmetrical distribution and higher exchange energy — extra stable like evenly arranged chairs.