Atomic Structure

Atomic structure is the foundation on which periodicity, chemical bonding, coordination chemistry and even organic reactivity are built, and it is one of the most formula-dense chapters in the NEET syllabus. Every year you can expect direct numerical questions on Bohr's equations, de Broglie wavelength, quantum numbers and electronic configurations, so both the concepts and the arithmetic shortcuts matter.

Subatomic Particles and Early Models

Matter is electrically neutral overall, yet it can be made to conduct, ionise and emit radiation — evidence that atoms are divisible. Discharge tube experiments at low pressure produced cathode rays, streams of negatively charged particles that behaved identically no matter which metal formed the cathode. Their charge-to-mass ratio (e/m ≈ 1.758 × 10¹¹ C kg⁻¹) was measured by deflecting them in electric and magnetic fields; combining this with the charge found from the oil-drop experiment (1.602 × 10⁻¹⁹ C) gave the electron mass, 9.11 × 10⁻³¹ kg. Using a perforated cathode, positively charged canal rays were observed; unlike cathode rays, their e/m depended on the gas used, since different gases give different positive ions. The lightest such particle, the proton, has mass 1.673 × 10⁻²⁷ kg. The neutron, discovered much later by bombarding beryllium with α-particles, is electrically neutral with mass just slightly greater than the proton's.

Quick bookkeeping conventions you must be fluent in:

• Atomic number (Z) = number of protons = number of electrons in a neutral atom.
• Mass number (A) = protons + neutrons; neutrons = A − Z.
• Isotopes: same Z, different A (¹H, ²H, ³H). Isobars: same A, different Z (¹⁴C and ¹⁴N). Isoelectronic species: same electron count (Na⁺, Mg²⁺, F⁻, Ne, O²⁻ all have 10 electrons).

Thomson pictured the atom as a uniform sphere of positive charge with electrons studded in it. This model explained neutrality but died with Rutherford's gold-foil experiment: most α-particles passed straight through a thin foil, a few were deflected, and roughly one in 20,000 bounced back through more than 90°. The only explanation was a tiny, dense, positively charged nucleus (radius ~10⁻¹⁵ m) with electrons occupying the vast empty space (atomic radius ~10⁻¹⁰ m) and revolving around it. Rutherford's planetary model, however, had a fatal flaw: an accelerating charged particle must continuously radiate energy, so the electron should spiral into the nucleus in a fraction of a second. It also could not explain why atoms give line spectra.

Light, Quanta and the Photoelectric Effect

Because atomic structure was decoded through light, you need the vocabulary of electromagnetic radiation. A wave is described by wavelength λ, frequency ν, and wavenumber ν̄ = 1/λ, with c = νλ where c = 3 × 10⁸ m s⁻¹ in vacuum. Classical wave theory handled diffraction and interference beautifully but failed on three fronts: black-body radiation, the photoelectric effect, and atomic spectra.

Planck's resolution was radical: energy is exchanged not continuously but in packets ("quanta") of size

E = hν = hc/λ, with h = 6.626 × 10⁻³⁴ J s.

Einstein extended this to light itself — a beam is a stream of photons, each carrying hν. This explains the photoelectric effect point by point:

1. Electron ejection from a metal surface is instantaneous above a threshold frequency ν₀; below ν₀, no electrons come out however intense the light.
2. The kinetic energy of ejected electrons depends on frequency, not intensity: ½mv² = hν − hν₀, where hν₀ = work function (W₀ or φ).
3. The number of electrons ejected (photocurrent) depends on intensity, i.e. on the number of photons striking per second.

Light therefore has a dual character — wave-like in propagation, particle-like in interaction with matter. A common numerical style: given λ of incident light and the work function in eV, compute maximum KE or the stopping potential (eV₀ = KEmax). Remember 1 eV = 1.602 × 10⁻¹⁹ J.

Atomic Spectra and the Bohr Model

When white light passes through a prism you get a continuous spectrum. But an excited gaseous atom emits only certain discrete wavelengths — a line emission spectrum, unique to each element and effectively an atomic fingerprint. For hydrogen, the lines fall into series (Lyman in UV, Balmer in visible, then Paschen, Brackett, Pfund in IR), all fitted by the Rydberg formula:

ν̄ = 1/λ = R_H (1/n₁² − 1/n₂²), R_H = 109677 cm⁻¹, n₂ > n₁.

Bohr explained this with a quantised planetary model for hydrogen-like species (one electron, nuclear charge Z):

• The electron moves only in certain stationary orbits where its angular momentum is quantised: mvr = nh/2π, n = 1, 2, 3…
• While in an orbit the electron does not radiate energy — this postulate simply overrules the classical objection.
• Radiation is absorbed or emitted only when the electron jumps between orbits: ΔE = E₂ − E₁ = hν.

The results worth memorising:

• Radius: rₙ = 0.529 (n²/Z) Å
• Energy: Eₙ = −13.6 (Z²/n²) eV = −2.18 × 10⁻¹⁸ (Z²/n²) J
• Velocity: vₙ ∝ Z/n
• Energies are negative because the bound electron is at lower energy than a free electron (taken as zero at n = ∞). The ionisation energy of H is therefore +13.6 eV.
• Number of spectral lines produced when an electron falls from level n to the ground state = n(n − 1)/2.

Bohr's model nailed the hydrogen spectrum and the spectra of He⁺, Li²⁺, Be³⁺, but it fails for multi-electron atoms, cannot explain fine structure or the splitting of lines in a magnetic field (Zeeman effect), and — most fundamentally — it violates the uncertainty principle by assigning the electron a definite orbit and definite speed simultaneously.

Wave-Particle Duality, Uncertainty, and the Quantum Mechanical Picture

De Broglie argued that if light can behave as particles, matter should behave as waves:

λ = h/p = h/mv

For an electron accelerated through V volts, λ = 12.27/√V Å, a shortcut worth remembering. Note that macroscopic objects have absurdly small wavelengths (a cricket ball has λ ~10⁻³⁴ m), which is why wave behaviour is only observable for electrons, neutrons and similar light particles. Interestingly, Bohr's quantisation condition follows naturally if the orbit circumference contains a whole number of electron wavelengths: 2πr = nλ.

Heisenberg's uncertainty principle states that position and momentum cannot both be known with arbitrary precision:

Δx · Δp ≥ h/4π, i.e. Δx · Δv ≥ h/4πm.

The uncertainty is not an instrumental limitation but an intrinsic property of matter waves. Its consequence: the idea of a sharply defined electron trajectory is meaningless, so "orbits" must be replaced by probability distributions.

The quantum mechanical model replaces orbits with the Schrödinger equation, Ĥψ = Eψ. Solving it for the hydrogen atom gives:

• Quantised energies — these come out of the mathematics rather than being assumed.
• Wave functions ψ (orbitals), each labelled by a set of quantum numbers.
• ψ², the probability density: the probability of finding the electron per unit volume at a point. An "orbital" is conventionally drawn as the boundary surface enclosing ~90% probability.

Quantum Numbers, Orbital Shapes and Energies

Four quantum numbers completely specify an electron in an atom.

1. Principal quantum number (n) = 1, 2, 3…: fixes the shell, the main energy level and the size. Maximum electrons in a shell = 2n²; number of orbitals in a shell = n².
2. Azimuthal / orbital angular momentum quantum number (l) = 0 to (n − 1): fixes the subshell and shape — l = 0 (s), 1 (p), 2 (d), 3 (f). Number of orbitals in a subshell = 2l + 1. Orbital angular momentum = √(l(l+1)) · h/2π.
3. Magnetic quantum number (mₗ) = −l to +l including 0: fixes the orientation in space (e.g. for l = 1, three values give pₓ, p_y, p_z).
4. Spin quantum number (mₛ) = +½ or −½: two possible spin orientations, giving the electron its intrinsic magnetic moment.

Shapes and nodes:

• s orbitals are spherically symmetric; size and number of nodes increase with n.
• p orbitals are dumb-bell shaped with two lobes and a nodal plane through the nucleus; the three p orbitals are mutually perpendicular and degenerate in an isolated atom.
• d orbitals (five of them) are mostly double dumb-bells (d_xy, d_yz, d_zx, d_x²−y²) with d_z² having a distinctive doughnut. Each has two nodal planes.
• Total nodes = n − 1; radial (spherical) nodes = n − l − 1; angular nodes = l.

For hydrogen, energy depends only on n, so 2s and 2p are degenerate. In multi-electron atoms, inter-electronic repulsion and shielding make energy depend on both n and l: within a shell, s < p < d < f. The ordering follows the (n + l) rule — lower (n + l) fills first, and for equal (n + l), the lower n fills first. That is why 4s (n + l = 4) fills before 3d (n + l = 5).

Filling Rules and Electronic Configurations

Three principles govern how electrons occupy orbitals in the ground state:

• Aufbau principle: orbitals fill in increasing order of energy — 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d.
• Pauli exclusion principle: no two electrons in an atom can have all four quantum numbers identical; hence an orbital holds at most two electrons, with opposite spins.
• Hund's rule of maximum multiplicity: within a set of degenerate orbitals, electrons occupy them singly with parallel spins before any pairing begins, because pairing costs repulsion energy.

Worked patterns to know: N is 1s²2s²2p³ (three unpaired electrons, so paramagnetic), while Ne (1s²2s²2p⁶) has every orbital filled and is diamagnetic. Two elements famously deviate from the straightforward Aufbau prediction because a half-filled or fully-filled d subshell is extra stable: chromium is [Ar]3d⁵4s¹ (not 3d⁴4s²) and copper is [Ar]3d¹⁰4s¹ (not 3d⁹4s²) — one electron is effectively transferred from 4s to complete the more symmetric, lower-repulsion d⁵ or d¹⁰ arrangement. The same logic extends to Mo ([Kr]4d⁵5s¹) and Ag ([Kr]4d¹⁰5s¹) in the row below.

Ions are configured by first writing the atom's configuration and then removing (for cations) or adding (for anions) electrons from the outermost shell, not necessarily the last-filled subshell — a distinction that trips up many students with transition metals. For Fe (Z = 26, [Ar]3d⁶4s²), Fe²⁺ is [Ar]3d⁶ (both 4s electrons are removed first, not the 3d electrons) and Fe³⁺ is [Ar]3d⁵, which is why Fe³⁺ is the more stable, half-filled ion. The magnetic behaviour of a species follows directly from the number of unpaired electrons in its configuration: any unpaired electron makes a species paramagnetic (weakly attracted into a magnetic field), while a species with all electrons paired is diamagnetic (weakly repelled).

Common Mistakes and Exam Traps

1. Removing d electrons before s electrons when forming cations. For transition-metal ions, always empty the outermost ns orbital first, then remove from (n−1)d if further ionisation is needed — writing Fe²⁺ as [Ar]3d⁴4s² is a common but wrong shortcut.
2. Forgetting the Cr and Cu exceptions. Predicting Cr as 3d⁴4s² or Cu as 3d⁹4s² by blindly following the (n+l) rule ignores the extra stability of half-filled and fully-filled d subshells — NEET repeatedly tests exactly this pair of exceptions.
3. Mixing up angular and radial nodes. Total nodes = n − 1 always, but angular nodes = l and radial nodes = n − l − 1; assuming all nodes in a p or d orbital are "the same kind" leads to wrong node-counting answers.
4. Treating the uncertainty principle as a measurement flaw. Δx·Δp ≥ h/4π is a fundamental property of matter waves, not a limitation of instruments — questions sometimes frame it as "our apparatus isn't precise enough", which is the wrong reasoning to select.