Subatomic Particles
| Particle | Symbol | Charge | Mass (kg) | Mass (u) |
|---|---|---|---|---|
| Electron | e^- | -1.6 x 10^(-19) C | 9.1 x 10^(-31) | 0.00055 |
| Proton | p^+ | +1.6 x 10^(-19) C | 1.67 x 10^(-27) | 1.0073 |
| Neutron | n^0 | 0 | 1.67 x 10^(-27) | 1.0087 |
Discovery Timeline
- Electron: J.J. Thomson (1897) — cathode ray experiment.
- Proton: E. Goldstein (1886) — canal rays.
- Neutron: James Chadwick (1932) — alpha particle bombardment of beryllium.
Thomson Model (Plum Pudding Model)
Atom as a sphere of positive charge with electrons embedded like plums in pudding. Failed to explain alpha particle scattering.
Rutherford's Nuclear Model
Alpha Particle Scattering Experiment
Gold foil bombarded with alpha particles. Observations:
- Most alpha particles passed straight through.
- A few were slightly deflected.
- Very few (1 in 20,000) bounced back.
Conclusions
- Atom is mostly empty space.
- Nucleus is small, dense, and positively charged.
- Electrons orbit the nucleus.
Drawbacks
- Could not explain stability of atom (accelerating electrons should radiate energy and spiral into nucleus).
- Did not explain atomic spectra.
Bohr's Model
Postulates
- Electrons revolve in certain stationary orbits (energy levels) with fixed energy.
- Angular momentum is quantized:
mvr = nh/(2pi). - Electrons can jump between orbits by absorbing or emitting energy.
Delta E = E_2 - E_1 = hf.
Energy of Electron in nth Orbit
E_n = -13.6/n^2 eV
Radius of nth Orbit
r_n = n^2 * a_0, where a_0 = 0.529 A (Bohr radius).
Velocity of Electron in nth Orbit
v_n = (2.18 x 10^6)/n m/s
Limitations
- Works only for hydrogen-like species (single electron).
- Could not explain fine structure, Zeeman effect.
- Violates Heisenberg's uncertainty principle.
Quantum Mechanical Model
de Broglie's Hypothesis
Matter has wave-particle duality. lambda = h/(mv) = h/p
Heisenberg's Uncertainty Principle
It is impossible to simultaneously measure both position and momentum with absolute precision.
Delta x * Delta p >= h/(4pi)
Schrodinger Wave Equation
H hat(psi) = E hat(psi) (time-independent).
psi^2 gives the probability density of finding an electron in a region.
Orbitals and Quantum Numbers
Quantum Numbers
Principal quantum number (n): n = 1, 2, 3, ...
Determines size and energy of orbital.
Azimuthal quantum number (l): l = 0, 1, 2, ..., n-1
Determines shape of orbital.
l = 0: s orbital (spherical)l = 1: p orbital (dumbbell)l = 2: d orbital (cloverleaf)l = 3: f orbital (complex)
Magnetic quantum number (m_l): m_l = -l, ..., 0, ..., +l
Determines orientation in space.
Spin quantum number (m_s): m_s = +1/2 or -1/2
Determines spin direction of electron.
Shapes of Orbitals
- 1s: Spherical, no nodes.
- 2s: Spherical, one radial node.
- 2p: Dumbbell shape (px, py, pz), one angular node.
- 3d: Cloverleaf shape (dxy, dxz, dyz, dx2-y2, dz2).
Electronic Configuration Rules
Aufbau Principle
Electrons fill orbitals in order of increasing energy.
Energy order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s ...
Pauli Exclusion Principle
No two electrons in an atom can have the same set of all four quantum numbers. An orbital can hold maximum 2 electrons with opposite spins.
Hund's Rule
Electrons fill degenerate orbitals singly first, with parallel spins, before pairing.
Electronic Configurations (Examples)
- H (Z=1):
1s^1 - He (Z=2):
1s^2 - C (Z=6):
1s^2 2s^2 2p^2 - Na (Z=11):
1s^2 2s^2 2p^6 3s^1 - Fe (Z=26):
1s^2 2s^2 2p^6 3s^2 3p^6 3d^6 4s^2
Exceptions: Cr (Z=24): [Ar] 3d^5 4s^1 (not 3d^4 4s^2).
Cu (Z=29): [Ar] 3d^10 4s^1 (not 3d^9 4s^2).
These exceptions arise due to extra stability of half-filled and fully-filled d-subshells.
Worked Examples
Example 1: Calculate the energy of an electron in the 2nd orbit of hydrogen.
Solution: E_2 = -13.6/4 = -3.4 eV.
Example 2: Write the electronic configuration of Cl (Z=17).
Solution: 1s^2 2s^2 2p^6 3s^2 3p^5.
Common Mistakes
- 4s vs 3d filling: 4s fills before 3d, but during ionization, 4s electrons are removed first.
- Orbit vs orbital: Orbit is a fixed circular path (Bohr). Orbital is a probability region (quantum).
- Aufbau violations: Cr and Cu are common exceptions to remember.
- Quantum number ranges:
lgoes from0ton-1,m_lgoes from-lto+l.
ISC Exam Focus
- Theory (70%): Atomic models, quantum numbers, electronic configuration rules, Schrodinger equation.
- Application (30%): Writing electronic configurations, finding quantum numbers of electrons.
- ISC frequently asks: "Write the quantum numbers for the last electron of ..." or "State and explain Hund's rule."
- Comparison of Bohr and quantum mechanical models.
Self-Test Questions
Q1: State Heisenberg's uncertainty principle.
Answer: Delta x * Delta p >= h/(4pi). Position and momentum cannot be measured simultaneously precisely.
Q2: Write the electronic configuration of K (Z=19).
Answer: 1s^2 2s^2 2p^6 3s^2 3p^6 4s^1.
Q3: What are the four quantum numbers for the last electron of oxygen (Z=8)?
Answer: Oxygen: 1s^2 2s^2 2p^4. Last electron: n=2, l=1, m_l=-1, m_s=-1/2 (or +1/2 depending on convention).
Q4: How many electrons can have n=3 and l=2?
Answer: l=2 means d orbital. d-subshell has 5 orbitals, each holding 2 electrons. Total = 10 electrons.
Q5: Differentiate between orbit and orbital. Answer: Orbit: fixed circular path, Bohr model, 2D. Orbital: 3D probability region, quantum model.
Q6: State Hund's rule with an example. Answer: Electrons fill degenerate orbitals singly before pairing. Example: Carbon has 2p^2 with both electrons in different 2p orbitals with parallel spins.
