Atomic Orbitals and Electronic Structure for JEE Main

Atomic structure and electronic configuration underpin all of chemistry, from periodicity to bonding to reactivity. JEE Main draws two to four questions from this chapter every year, testing quantum numbers, orbital shapes, filling rules, and their exceptions. The material rewards methodical memorisation paired with understanding the underlying logic.

Quantum Numbers: The Four Descriptors

Every electron in an atom is described by four quantum numbers. Principal quantum number n (1, 2, 3, ...): determines shell and energy (for hydrogen). Azimuthal quantum number l (0 to n−1): determines subshell — l = 0 is s, 1 is p, 2 is d, 3 is f. Magnetic quantum number m_l (−l to +l): determines orbital orientation; there are (2l+1) orbitals per subshell. Spin quantum number m_s (+½ or −½): each orbital holds two electrons with opposite spins (Pauli exclusion principle). The number of orbitals in the nth shell is n²; the maximum electrons in the nth shell is 2n². See the atomic structure foundations in our atomic structure guide.

Shapes and Nodes of Orbitals

s-orbitals are spherically symmetric. The 1s has no node; 2s has one spherical node and a larger radius. p-orbitals are dumbbell-shaped with one nodal plane. d-orbitals have four-lobed (cloverleaf) shapes (four of them) plus d_z² which is unique (dumbbell with torus). f-orbitals have complex shapes with three nodal planes. The number of radial nodes = n − l − 1; total nodes = n − 1. The d_x²-y² and d_z² point directly along axes (relevant to crystal field theory); d_xy, d_xz, d_yz point between axes.

Aufbau Principle and Orbital Energy Order

Fill orbitals in increasing energy: 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p ... The (n+l) rule: the orbital with lower (n+l) is filled first; if equal, lower n first. Hund's rule: in degenerate orbitals, electrons occupy them singly before pairing, with parallel spins. Pauli exclusion: no two electrons can have all four quantum numbers identical. These three rules — Aufbau, Hund, Pauli — govern all electronic configurations.

Exceptions: Chromium and Copper

Cr (Z=24): expected [Ar] 3d⁴ 4s², actual [Ar] 3d⁵ 4s¹ — half-filled 3d is extra stable. Cu (Z=29): expected [Ar] 3d⁹ 4s², actual [Ar] 3d¹⁰ 4s¹ — fully-filled 3d is extra stable. These are the two most-tested exceptions. The general rule: half-filled (3d⁵) and fully-filled (3d¹⁰) subshells have extra stability due to exchange energy. Similarly, Mo and Pd in period 5. Recognise these at a glance — JEE frequently asks for the correct configuration of these elements.

Ionisation and Effective Nuclear Charge

Ionisation removes electrons starting from the outermost, highest-energy orbital. Successive ionisation energies (IE₁ < IE₂ < IE₃ ...) show a large jump when a complete subshell is first breached — this jump identifies the group of the element. The effective nuclear charge Z_eff = Z − σ (Slater's rules give σ). Z_eff explains why ionisation energy generally increases across a period and why d-block contraction compresses atomic radii across the transition series. After reviewing atomic structure, take a free mock test to apply these concepts under time.