Structure of atom
Class 11 · Updated 2026-10-02. Published for practice.
What is inside an atom
An atom is not the final piece. Electrons, protons, and neutrons sit inside it. Other short-lived particles show up in nuclear physics; Class 11 usually sticks to e-, p+, n.
Atomic number Z = number of protons. In a neutral atom, electrons = protons = Z.
Mass number A = protons + neutrons. Neutrons = A − Z.
Isotopes: same Z, different A (same element, different mass). Hydrogen’s common set: 1H, 2H, 3H.
Isobars: same A, different Z (different elements, same mass number). Example pattern: 14C and 14N.
How the particles were found
Cathode rays (discharge tube, low pressure, high voltage): travel straight, deflected toward the positive plate → negative particles. Thomson measured e/m for the electron.
Millikan’s oil-drop work gave the elementary charge scale. The value you write in exams is e ≈ 1.6 × 10-19 C. Use the value your board table prints if they give one.
Anode / canal rays: positive particles; their e/m depends on the gas in the tube. Lightest positive ion from hydrogen → proton.
Neutron: Chadwick (1932). Be bombarded with α-particles → neutral particles with mass close to the proton.
Models you must compare
Thomson (plum pudding): positive sphere with electrons stuck in it. Explains overall neutrality. Fails Rutherford’s scattering results.
Rutherford: most α-particles go straight → mostly empty space. Rare large deflections → tiny, dense, positive nucleus. Electrons outside.
Rutherford’s hole: an orbiting electron should radiate and spiral in (classical EM). Atom would not be stable.
Bohr (for H and one-electron ions): electrons only in allowed orbits; angular momentum mvr = nh/2π; no radiation while in an allowed orbit; jumps between orbits exchange energy as photons.
Bohr works for H-like spectra. It fails multi-electron atoms, fine structure, Zeeman/Stark detail, and it clashes with the uncertainty principle.
Light, photoelectric effect, dual nature
c = νλ. Wave number = 1/λ.
Planck: energy comes in packets. E = hν. h ≈ 6.626 × 10-34 J s (write the value your book uses).
Photoelectric effect: need ν ≥ ν0 (threshold). KE of ejected electron = hν − hν0. Intensity changes how many electrons leave, not their max KE.
de Broglie: matter also has wavelength λ = h/mv = h/p. Useful for electrons; everyday objects have tiny λ, so you do not “see” their wave side.
Heisenberg: you cannot pin exact position and exact momentum of a tiny particle at once. Δx · Δp ≥ h/4π.
Hydrogen line spectrum
Discharge through H2 → line spectrum. Rydberg form: wave number = R(1/n12 − 1/n22), with n2 > n1.
n1 = 2 → Balmer (visible). n1 = 1 → Lyman (UV). Higher series sit further into IR.
R is the Rydberg constant. Use the value printed in your exam data if they give one.
Four quantum numbers
n (principal): shell. Size and energy ladder. n = 1, 2, 3…
l (azimuthal): subshell / shape. l = 0 → s, 1 → p, 2 → d, 3 → f. For a given n, l runs 0 to n−1. Orbitals in a subshell: 2l + 1.
mₗ (magnetic): orientation. For a given l, mₗ = −l … 0 … +l.
mₛ (spin): +1/2 or −1/2.
One orbital holds at most two electrons, opposite spins (Pauli).
Orbital shapes and filling order
s: spherical. p: dumbbell (pₓ, pᵧ, p_z). d: five orbitals (d_xy, d_yz, d_zx, d_x2−y2, d_z2).
Aufbau: fill lower energy first. Common order: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p …
(n + l) rule: lower (n + l) fills first; if tied, lower n fills first.
Hund: in a subshell, put one electron in each orbital (same spin) before pairing.
Exam trap: Cr and Cu are exceptions students are expected to know (half-filled / filled d preference). Write Cr: [Ar] 3d5 4s1, Cu: [Ar] 3d10 4s1.