Chapter Summary

This chapter traces the journey from the discovery of sub-atomic particles to the quantum mechanical model of the atom. Here's everything you need to remember.

1. Sub-atomic Particles

Particle Symbol Charge Mass
Electron e−e^- −1.6×10−19-1.6 \times 10^{-19} C 9.109×10−319.109 \times 10^{-31} kg
Proton p+p^+ +1.6×10−19+1.6 \times 10^{-19} C 1.673×10−271.673 \times 10^{-27} kg
Neutron nn 0 1.675×10−271.675 \times 10^{-27} kg
  • Thomson discovered the electron (1897) using cathode rays
  • e/me/m ratio of electron = 1.758×10111.758 \times 10^{11} C/kg
  • Millikan's oil drop experiment determined charge of electron
  • Goldstein discovered the proton (canal rays)
  • Chadwick discovered the neutron (1932)

2. Atomic Models

  • Thomson's model: Atom is a positive sphere with electrons embedded (plum pudding model) — failed to explain Rutherford's experiment
  • Rutherford's model: Nucleus is small, dense, positively charged; electrons revolve around it — failed to explain stability (electrons should spiral in) and line spectra

3. Atomic Number, Mass Number, Isotopes & Isobars

  • Atomic number (ZZ) = number of protons
  • Mass number (AA) = protons + neutrons = Z+NZ + N
  • Notation: ZAX{}^A_Z X
  • Isotopes: Same ZZ, different AA (e.g., 11{}^1_1H, 12{}^2_1H, 13{}^3_1H)
  • Isobars: Same AA, different ZZ (e.g., 1840{}^{40}_{18}Ar, 2040{}^{40}_{20}Ca)
  • Isotones: Same number of neutrons

4. Electromagnetic Radiation

  • c=νλc = \nu\lambda where c=3×108c = 3 \times 10^8 m/s
  • Wave number: νˉ=1/λ\bar{\nu} = 1/\lambda
  • EM spectrum (increasing energy): Radio < Microwave < IR < Visible < UV < X-ray < γ\gamma-ray
  • Visible light: 380 nm (violet) to 750 nm (red)

5. Planck's Quantum Theory & Photoelectric Effect

E=hν=hcλE = h\nu = \frac{hc}{\lambda}

  • h=6.626×10−34h = 6.626 \times 10^{-34} J s
  • Photoelectric equation: hν=hν0+12mev2h\nu = h\nu_0 + \frac{1}{2}m_e v^2
  • Work function W0=hν0W_0 = h\nu_0
  • Threshold frequency ν0\nu_0: minimum frequency for electron ejection
  • KE depends on frequency (not intensity); number of electrons depends on intensity

6. Atomic Spectra

Rydberg formula: 1λ=RH(1n12−1n22)\frac{1}{\lambda} = R_H\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)

RH=1.097×107R_H = 1.097 \times 10^7 m−1^{-1}

Series n1n_1 Region
Lyman 1 UV
Balmer 2 Visible
Paschen 3 IR
Brackett 4 IR
Pfund 5 Far IR

Total spectral lines from level nn: n(n−1)2\frac{n(n-1)}{2}

7. Bohr's Model

En=−13.6Z2n2 eV,rn=n2a0Z,vn=2.18×106Zn m/sE_n = -\frac{13.6 Z^2}{n^2} \text{ eV}, \quad r_n = \frac{n^2 a_0}{Z}, \quad v_n = \frac{2.18 \times 10^6 Z}{n} \text{ m/s}

  • a0=0.529a_0 = 0.529 Å (Bohr radius)
  • E1=−13.6E_1 = -13.6 eV (hydrogen ground state)
  • Valid for H and H-like species (He+^+, Li2+^{2+}, etc.)
  • Limitations: Fails for multi-electron atoms, fine structure, Zeeman/Stark effects

8. de Broglie & Heisenberg

λ=hmv=h2mKE\lambda = \frac{h}{mv} = \frac{h}{\sqrt{2mKE}}

Δx⋅Δp≥h4π\Delta x \cdot \Delta p \geq \frac{h}{4\pi}

  • Wave nature significant only for microscopic particles
  • Verified by Davisson & Germer (electron diffraction)
  • Uncertainty principle makes precise orbits meaningless → orbitals

9. Quantum Numbers

QN Symbol Values Determines
Principal nn 1, 2, 3, … Shell, size, energy
Azimuthal ll 0 to n−1n-1 Subshell, shape
Magnetic mlm_l −l-l to +l+l Orientation
Spin msm_s +1/2,−1/2+1/2, -1/2 Spin direction
  • Orbitals per subshell: 2l+12l + 1
  • Orbitals per shell: n2n^2
  • Max electrons per shell: 2n22n^2

10. Shapes & Nodes

  • s: spherical, p: dumbbell, d: double dumbbell/dz2d_{z^2} special
  • Radial nodes =n−l−1= n - l - 1, Angular nodes =l= l, Total =n−1= n - 1

11. Electronic Configuration Rules

  • Aufbau: Fill in order of increasing (n+l)(n + l); if same, lower nn first
  • Pauli: Max 2 electrons per orbital, opposite spins
  • Hund's: Maximise unpaired electrons in degenerate orbitals
  • Exceptions: Cr: 3d54s13d^5 4s^1 (not 3d44s23d^4 4s^2), Cu: 3d104s13d^{10} 4s^1 (not 3d94s23d^9 4s^2)
  • Half-filled (d5d^5) and fully-filled (d10d^{10}) subshells have extra stability
  • During ionisation of transition metals, 4s electrons are removed first

For JEE/NEET/Competitive Exams

  • Isoelectronic Species: Atoms or ions with the same number of electrons. For these, the one with the higher ZZ (protons) will have the smallest radius due to stronger attraction.
  • Velocity Comparisons: v∝Znv \propto \frac{Z}{n}. This is often used in ratio questions comparing HH and He+He^+.
  • Shortcut for K.E.K.E.: If an electron is accelerated by VV volts, its λ=12.27V\lambda = \frac{12.27}{\sqrt{V}} Å. This saves minutes during the exam!
  • Half-Filled Stability: Always check if a configuration can reach d5d^5 or d10d^{10} by shifting an ss electron (e.g., CrCr and CuCu). This is the most common trick question.
  • Ionization Energy: Remember that I.E.=E∞−E1=+13.6Z2 eVI.E. = E_{\infty} - E_1 = +13.6 Z^2 \text{ eV} for H-like species.

Gyan Path: Chapter 2 is the gateway to understanding the Periodic Table and Chemical Bonding. Master the 'Quantum Number' logic now, and the next few chapters will feel like a breeze!