Structure of Atom
Domain 2: Structure of Atom
This domain tests the quantum-mechanical description of atoms: quantum numbers, orbital energies, electronic configurations, and evidence for quantisation from spectra, the photoelectric effect, de Broglie waves, and the Heisenberg principle.
Core rules
- For principal quantum number n, l=0 to n−1; m_l=−l to +l; m_s=±1/2. Orbital count = n^2; maximum electrons = 2n^2.
- Aufbau fills lower (n+l) first; for equal (n+l), lower n first. Pauli allows a maximum of two electrons with opposite spin; Hund keeps maximum unpaired spins in degenerate orbitals.
- Cr [Ar]3d5 4s1 and Cu [Ar]3d10 4s1 are stability exceptions.
- Bohr energy for H-like species: E_n = −13.6 Z^2/n^2 eV; transition energy is the difference; ΔE = hν = hc/λ.
- de Broglie λ = h/mv; Heisenberg ΔxΔp ≥ h/4π; orbitals are probability distributions, not fixed paths.
Worked example
For the H atom transition n=3 to 2: E3=−13.6/9=−1.51 eV; E2=−13.6/4=−3.40 eV. ΔE=1.89 eV. λ=1240/1.89≈656 nm using λ(nm)=1240/E(eV). This is the red Balmer line; the negative sign shows the atom emits energy.
Traps
- Writing 4s before 3d in filling but assuming 4s remains lower after filling; 3d is lower in energy for transition-metal cations.
- Violating Pauli in orbital diagrams.
- Confusing the number of orbitals with maximum electrons.
- Using the Rydberg formula for multi-electron atoms.
- Ignoring that m_l depends on l.