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Atoms

Bohr's model and the hydrogen spectrum: radius, energy and the spectral series. Scaling with Z and n answers most questions.

Questions in the bank
92
q/paper in 2025–26
0.60
Numeric answer
32%
Notes pages
4

Tier: Long tail

When you’ll see it

A hydrogen-like ion's orbit, energy level, spectral line or transition, or alpha scattering and the distance of closest approach.

How this chapter is tested

Most questions rest on three results of Bohr's model: the radius goes as n²/Z, the speed as Z/n, and the energy as −13.6 Z²/n² eV. So many are ratios that the constants cancel and the working is short.

The pages go from Rutherford's experiment and Bohr's postulates, to the orbits, to the spectral series, to transitions and X-rays. Rutherford's scattering and X-rays are asked only now and then; the orbits, the series and the transitions carry the chapter.

Marks are lost on reading the question: the second excited state taken as n = 2, the series limit taken as the longest line, or a photon treated like an electron that can hand over part of its energy. Photon energies in eV come from Dual Nature, and closest approach is an energy balance from Electrostatics.

The sub-skills

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

  • Rutherford scattering and Bohr's postulates

    Closest approach from K = k(2e)(Ze)/r₀; Bohr allows only orbits with L = nh/2π, and light comes out only in a jump between them.

  • Bohr orbits

    r ∝ n²/Z, v ∝ Z/n, E = −13.6 Z²/n² eV with K = −E; frequency, current and magnetic moment are built from r and v.

  • Spectral series and line ratios

    1/λ = RZ²(1/n_f² − 1/n_i²); each series ends on one lower level; the first member is the longest line and the limit the shortest; a ratio needs only the brackets.

  • Transitions, excitation and X-rays

    A photon carries the energy gap and is absorbed only if it matches one; a sample at level n gives n(n − 1)/2 lines; the X-ray cut-off is hc/eV and ignores the target.

Traps to expect

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

  • Excited states are one behind n

    The first excited state is n = 2 and the second is n = 3. Reading the second excited state as n = 2 is wrong every time.

  • Series limit and first line

    The limit is the shortest wavelength of a series and the first member the longest. The Balmer limit is 4/R, not 1/R.

  • Photon or electron

    A photon is absorbed only if its energy matches a gap. An electron can hand over part of its energy and keep the rest.

  • Z or Z²

    The radius has Z to the first power and the energy has Z². The same jump in He⁺ releases four times the energy it does in hydrogen.

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.

Atoms notes

Drill every Atoms question

92 questions from the bank, across 4 subtopics.

Drill the 92 questions

Drill one subtopic at a time

The 4 subtopics, in teaching order.

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