Atomic Structure — JEE Main & Advanced Notes

Start by counting electrons. H, He⁺ and Li²⁺ each have one electron, so the hydrogen-like energy formula applies. Neutral helium has two: substituting Z = 2 into that formula does not describe its spectrum.

Rutherford scattering supports a small, concentrated positive nucleus. Bohr introduced discrete energies to explain hydrogen's spectral lines. A quantum orbital describes a state and its probability distribution, not a circular track followed by an electron. The simple Bohr values are useful approximations; they omit fine structure and other corrections.

Study route: energy levels → photons → matter waves → quantum numbers → electronic configurations. Keep electron energy, photon energy and ionisation energy separate.

• Hydrogen-like energy: Eₙ = −13.6 Z²/n² eV, with zero energy assigned to a separated electron and nucleus.
• Bohr radius: rₙ = 0.529 n²/Z Å. Convert 1 Å to 10⁻¹⁰ m when using SI units.
• Ionising from level n requires +13.6 Z²/n² eV. It is the energy needed to reach E = 0.
• For a downward transition, the atom's energy change is negative but emitted photon energy is positive: Eγ = Eᵢ − E𝒇 = hc/λ.
• Use hc ≈ 1240 eV nm when energy is in eV and wavelength in nm. Do not combine this number with joules.
• For hydrogen, transitions ending at n = 1 form the Lyman series; those ending at n = 2 form Balmer. The first Balmer lines are visible, but the series limit is ultraviolet, so the entire series is not visible.

At fixed Z, increasing n makes a bound energy less negative and increases the Bohr radius. For a fixed final level, the nearest higher level gives the longest emitted wavelength; the series limit gives the shortest.

The de Broglie relation is λ = h/p. In nonrelativistic calculations p = mv. For an electron accelerated from rest through V volts, eV = p²/(2mₑ), giving λ ≈ 12.27/√V Å. This shortcut assumes negligible initial kinetic energy and nonrelativistic speed.

Position and momentum spreads along the same axis satisfy Δx Δpₓ ≥ ℏ/2 = h/(4π). For a nonrelativistic particle, Δpₓ = m Δvₓ. These are uncertainties, not the particle's position or speed. A negative velocity does not mean a negative uncertainty.

Useful constants: h = 6.626 × 10⁻³⁴ J s; mₑ = 9.109 × 10⁻³¹ kg; 1 eV ≈ 1.602 × 10⁻¹⁹ J. State any rounding used.

• n = 1, 2, 3, …; l = 0 through n − 1; mₗ = −l through +l; mₛ = ±½. Check these limits in this order.
• For s, p, d and f subshells, l is 0, 1, 2 and 3 respectively. A subshell contains 2l + 1 orbitals and can hold 2(2l + 1) electrons.
• A shell has n² orbitals and capacity 2n² electrons. Capacity does not mean that a particular atom actually has that many electrons in the shell.
• For hydrogen-like orbitals, radial nodes = n − l − 1; angular nodes = l; total = n − 1.

Pauli permits two opposite-spin electrons per orbital. Hund's rule spreads electrons singly, with parallel spins, across degenerate orbitals before pairing. The n + l filling sequence is a useful guide, not an exception-free energy law for every ion. Ground-state Cr is [Ar] 3d⁵4s¹ and Cu is [Ar] 3d¹⁰4s¹.

For transition-metal cations, remove the outer ns electrons before (n − 1)d electrons. Fe is [Ar] 3d⁶4s²; Fe²⁺ is [Ar] 3d⁶ and Fe³⁺ is [Ar] 3d⁵. Do not reverse the neutral filling sequence mechanically.

• Convert wavelength units before substituting constants.
• Identify one-electron species before using Z² scaling.
• Do not equate an orbital with an orbit.
• Do not describe every Balmer line as visible.
• Write the charge and electron count before an ion's configuration.

Next use orbital filling to explain chemical bonding and molecular orbitals, or return to all JEE Chemistry chapters. Try the worked problems again with the answers closed before moving to timed practice.

For the energy-level model and its limits, see OpenStax: the Bohr model. The explanations and problems here were independently written for LearnAtMyPlace.