PYQ Vault

Playbook

Structure of Atom

Photons, the Bohr model and the hydrogen spectrum, de Broglie and uncertainty, then quantum numbers and electron configuration. Half calculation, half counting electrons and orbitals.

Questions in the bank
130
q/paper in 2025–26
1.23
Calculation
42%
Notes pages
7

Strand: Calculate

When you’ll see it

A photon's energy or wavelength, a Bohr orbit or a spectral line, a de Broglie wavelength, an uncertainty, or a set of quantum numbers, nodes or orbital energies to count and order.

How this chapter is tested

The chapter has two halves. The calculation half runs on a handful of relations: E = hν = hc/λ, the photoelectric equation, the Bohr radius and energy, the Rydberg equation and the de Broglie wavelength with the uncertainty principle. Each is one line once the units are right.

Units decide those marks. Energies arrive in eV and leave in joules, masses must be in kg because h is in J s, and a wavenumber in cm⁻¹ needs c in cm s⁻¹. Numeric answers are often asked as a coefficient of a power of ten, so read which power the stem fixes.

The counting half is quantum numbers, nodes and configurations. It is quick but exact: l stops at n − 1, radial nodes are n − l − 1, the (n + l) rule breaks a tie by the lower n, and hydrogen ignores the rule altogether.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Photons and the photoelectric effect

    E = hν = hc/λ = hcν̄; hν = hν₀ + ½mv²; intensity changes the number of electrons, frequency their energy.

  • Bohr orbits

    rₙ = 52.9 n²/Z pm, Eₙ = −13.6 Z²/n² eV; KE = −E and PE = 2E; only one-electron species qualify.

  • Hydrogen spectrum

    ν̄ = RZ²(1/n₁² − 1/n₂²); the series is named by the landing level; first line is the longest wavelength, the series limit the shortest.

  • de Broglie and uncertainty

    λ = h/mv = h/√(2mK); n whole waves fit a Bohr orbit, so λ grows as n; Δx·mΔv ≥ h/4π.

  • Quantum numbers

    Allowed values of n, l, mₗ, mₛ; a subshell holds 2(2l + 1) electrons; orbital angular momentum √(l(l + 1)) h/2π.

  • Orbitals, nodes and plots

    Radial nodes n − l − 1, angular nodes l; ψ² peaks at the nucleus for 1s while 4πr²ψ² peaks at a₀.

  • Orbital energies and configurations

    (n + l) rule for many-electron atoms, n alone for hydrogen-like ones; Cr and Cu take half-filled and filled d subshells.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • Radius scaled as n

    The radius goes as n², so the sixth orbit of H is 36/16 times the fourth, not 6/4. The de Broglie wavelength in an orbit is the one that goes as n.

  • eV and J on different footings

    Convert with 1 eV = 1.602 × 10⁻¹⁹ J before subtracting a work function from hν. Mixing them gives an answer off by a huge power of ten.

  • Lines from one electron

    n(n − 1)/2 counts the lines a large sample can emit. A single electron cascading from n = 5 gives at most 4.

  • Aufbau applied to hydrogen

    In a one-electron atom 2s and 2p have the same energy and 4s lies above 3d. The (n + l) order holds only for many-electron atoms.

  • The wrong node formula

    Radial nodes are n − l − 1, not n − l. A 3s orbital has two radial nodes; a nodal plane is an angular node.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Structure of Atom notes

Drill every Structure of Atom question

130 questions from the bank, across 7 subtopics.

Drill the 130 questions

Drill one subtopic at a time

The 7 subtopics, in teaching order.

Related playbooks

Often paired with this one — the technique or the trap overlaps. Drill these next.