Theme E — Nuclear and Quantum Physics
E.1.7 The Bohr Model of Hydrogen — IB Physics HL Revision Notes & Topical Questions
5 min read 10 parts Lesson 9 of 45 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
E.1.7 The Bohr Model of Hydrogen — IB PHYSICS HL notes: Describe the Bohr model of hydrogen, its quantised angular momentum and energy levels E = −13.6/n² eV, and the spectral series.Why hydrogen — it is the simplest atom, ideal for investigating electron energy levelsTransitions…
- Lyman series
- Balmer series
- Paschen (Ritz–Paschen) series
- Pfund series
- Circular orbits
- Allowed orbits
Section 1 of 10Hydrogen line series
Hydrogen line series
Why hydrogen
- Why hydrogen it is the simplest atom, ideal for investigating electron energy levels
Transitions
- Transitions electrons jump between specific levels and emit photons of specific energy
Lyman series
- Lyman series transitions to n = 1, giving the highest-energy, shortest-wavelength photons in the ultraviolet
Balmer series
- Balmer series transitions to n = 2, with four lines in the visible region
- (red 656 nm from n = 3 to 2, blue-green 486 nm from n = 4 to 2)
Paschen (Ritz–Paschen) series
- Paschen (Ritz–Paschen) series transitions to n = 3, in the infrared
Pfund series
- Pfund series the lowest-energy, longest-wavelength photons, in the infrared
Crowding
- Crowding lines in a series converge as n increases
Section 2 of 10Bohr's postulates
1Circular orbits
- Circular orbits the electrostatic force provides the centripetal force, ke2/r2 = mev2/r
2Allowed orbits
- Allowed orbits only fixed orbits with certain radii exist
3Quantised angular momentum
- Quantised angular momentum mevr = nh/2π with n = 1, 2, 3, …
4Stationary states
- Stationary states an electron in an allowed orbit does not radiate
5Emission and absorption
- Emission and absorption a photon is emitted or absorbed only when the electron jumps between orbits, hf = Ei − Ef
6Problem solved
- Problem solved a classical orbiting electron should radiate and spiral into the nucleus, and the nuclear model could not explain line spectra
Section 3 of 10Energy levels
Equation
- En = −13.6/n2 eV, equal to −2.18 × 10−18/n2 J
Sign
- Sign negative because the electron is bound
Ground state
- Ground state n = 1 with E = −13.6 eV, so 13.6 eV is the ionisation energy
High n
- High n the energy approaches zero from below and the levels converge
Transition
- Transition hf = 13.6(1/nf2 − 1/ni2) eV
Frequency
- Frequency f = E/h with E converted to joules (1 eV = 1.6 × 10−19 J)
Section 4 of 10Radii and speeds
Radii
- Radii rn = n2r1 with the first Bohr radius r1 = 5.29 × 10−11 m
Speeds
- Speeds vn = v1/n with v1 ≈ 2.19 × 106 m s−1
Check
- Check from mevr = nh/2π, n = 1 and r = 0.529 × 10−10 m, v = h/(2πmer) = 2.2 × 106 m s−1
Section 5 of 10Angular momentum
Definition
- Definition a vector equal to the momentum times the radial distance for a circular orbit
- Its direction is normal to the plane of the orbit, given by the corkscrew rule
Linear analogy
- Linear analogy in rotation the momentum is moment of inertia times angular speed
Bohr condition
- L = nh/2π, so L is constant for an electron in a given orbit
Section 6 of 10De Broglie explanation of quantisation
Matter wave
- Matter wave an electron with momentum p = mv has wavelength λ = h/p
Circular orbit
- Circular orbit the matter wave wraps into a circle
Allowed orbits
- Allowed orbits the wave overlaps in phase after one circuit, forming a standing wave by constructive interference
Forbidden orbits
- Forbidden orbits a wave that does not overlap in phase gives destructive interference
Condition
- Condition the circumference is a whole number of wavelengths, nλ = 2πr
Result
- Result substituting λ = h/mv gives mvr = nh/2π, the Bohr condition
Section 7 of 10Evidence and limits
Franck–Hertz experiment
- Franck–Hertz experiment electrons passing through mercury vapour lose energy in discrete amounts, supporting discrete levels
Spectra
- Spectra the hydrogen spectrum gives direct evidence for En ∝ 1/n2
Hydrogen-like ions
- Hydrogen-like ions one-electron ions have En = −13.6Z2/n2 eV
Limits
- Limits it fails for atoms with more than one electron, does not explain line intensities or fine structure,
- and treats the electron as a particle in a definite orbit
Section 8 of 10More from the specification
More from the specification
Rutherford Alpha Particle Scattering
- Bombarding thin gold foil with positively charged alpha particles revealed that most pass undeflected while a small fraction rebound through large angles.
Nuclear Model of the Atom
- The large deflection of alpha particles demonstrated that the atom's positive charge and nearly all its mass are concentrated in a dense, central atomic nucleus.
Strong Nuclear Force
- Protons in the nucleus are held together against electrostatic Coulomb repulsion by the short-range, attractive strong nuclear force acting between nucleons.
Bohr Quantisation Model
- Bohr modified the planetary atomic model by proposing that electrons orbit only in discrete non-radiating shells, explaining the sharp line spectra of light.
Scattering
- Deflection of particles from their original path.
Charge
- Quantity of electricity in coulombs, Q = It.What the symbols mean: Q = charge (C) · I = current (A) · t = time (s)
Density
- Mass per unit volume.
Alpha particle
- Helium nucleus, charge +2.
Rutherford scattering
- Scattering of charged particles by a nucleus through electrostatic repulsion alone.
Nuclear density
- The same for all nuclei, ρ = 3u/(4πR03), about 2 × 1017 kg m−3.
Section 9 of 10Key terms
| Term | Meaning |
|---|---|
| Bohr model | A model in which electrons in hydrogen move in fixed orbits with quantised angular momentum. |
| Bohr condition | mevr = nh/2π. |
| Lyman series | Transitions to the ground state n = 1, in the ultraviolet. |
| Balmer series | Transitions to n = 2, including the visible lines. |
| Ionisation energy | The energy needed to remove the electron from the ground state, 13.6 eV for hydrogen. |
| Matter wave | The wave associated with a moving particle, λ = h/p. |
Section 10 of 10Exam technique
1
Giving the ground-state energy as positive — bound-state energies are negative.
2
Using n for the number of electrons — it labels the orbit.
3
Forgetting the photon energy is the difference between levels, not the level energy itself.
4
Believing the Bohr model works for all atoms — it applies to hydrogen-like systems only.
5
Thinking the electron radiates while in an orbit — it radiates only when it jumps.
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