Theme E — Nuclear and Quantum Physics
E.1.1 Rutherford’s Gold Foil Experiment — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 3 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.1.1 Rutherford's Gold Foil Experiment — IB PHYSICS SL notes: Describe the alpha-scattering experiment and explain how its results led to the nuclear model of the atom.Known facts — the electron had been discovered (Thomson, 1897) and atoms were known to be electrically neutralP…
- Plum pudding model
- Alpha particle
- Source in a lead container
- Evacuated chamber
- Thin gold foil
- Narrow beam
Section 1 of 9The atom before 1911
The atom before 1911
Known facts
- Known facts the electron had been discovered (Thomson, 1897) and atoms were known to be electrically neutral
Plum pudding model
- Plum pudding model a sphere of diffuse positive charge about 10−10 m across with electrons embedded in it
- Positive charge and most of the mass are spread through the whole atom.
- A charged particle passing through should feel only weak spread-out forces and deflect by very small angles.
The test
- Rutherford, with Geiger and Marsden, fired alpha particles at a very thin gold foil
Alpha particle
- Alpha particle a helium nucleus with charge +2e and mass about 4 u
Section 2 of 9Apparatus
Apparatus
Source in a lead container
- Source in a lead container alpha particles are emitted in all directions and lead absorbs them
- A long narrow hole at the front lets a concentrated, collimated beam escape.
Evacuated chamber
- Evacuated chamber alpha particles are highly ionising and travel only about 5 cm in air
- The vacuum stops scattering and absorption by air molecules.
Thin gold foil
- Thin gold foil about 10−6 m thick, only a few hundred atoms
- A thicker foil would stop the alpha particles.
- A thin foil ensures each particle is deflected by at most a single nucleus.
- Gold is very malleable, so it can be hammered extremely thin, and it has a large nuclear charge.
Narrow beam
- Narrow beam the scattering angle is well defined
Movable detector
- Movable detector a zinc sulfide screen viewed with a microscope was moved around a circle centred on the foil
- Each alpha particle produced a tiny flash of light that could be counted.
- The number of particles at each angle was recorded.
Section 3 of 9Observations and conclusions
| Observation | Conclusion |
|---|---|
| Most alpha particles passed straight through undeflected | Most of the atom is empty space; the deflecting charge is concentrated, not spread out |
| Some were deflected through small angles (less than about 10°) | The atom has a positive nucleus, since two positive charges repel |
| A small fraction (about 1 in 104) were deflected through more than 90°, a very few almost straight back | The nucleus is extremely small and dense, holding most of the mass and all the positive charge |
Rutherford's remark
- Rutherford's remark back-scattering was like a 15-inch shell fired at tissue paper coming back
Force needed
- Force needed back-scattering requires a huge force, so a large charge must be concentrated in a tiny volume
Graph
- Graph the number of particles detected is largest at small angles and drops quickly as the deflection angle rises
Section 4 of 9The nuclear model
Nucleus
- Nucleus a tiny central region containing all the positive charge and almost all the mass
Size
- Size the nuclear radius is of order 10−15 m (femtometres), about 105 times smaller than the atom
Electrons
- Electrons they occupy the mostly empty space around the nucleus
Estimating size
- Estimating size the fraction scattered through large angles measures the fraction of the foil area blocked by nuclei
- A small fraction means nuclei are tiny compared with atoms.
Section 5 of 9Why electrons do not matter
Mass ratio
- Mass ratio alpha particles are about 7300 times more massive than electrons, so electrons barely deflect them
Deflecting force
- Deflecting force the electrostatic repulsion F = kQq/r2 between the positive alpha particle and the positive nucleus
Head-on path
- Head-on path a particle aimed directly at a nucleus is stopped and reversed
Off-centre path
- Off-centre path it is deflected through a smaller angle
Impact parameter
- Impact parameter the perpendicular distance by which an undeflected path would miss the nucleus
- A small impact parameter means a large deflection.
Section 6 of 9Limitations of the nuclear model
1Stability
- Stability an orbiting electron accelerates and should radiate energy and spiral into the nucleus, so atoms should not be stable
2Spectra
- Spectra the model did not explain the discrete line spectra of atoms
3Later models
- Later models these problems were addressed by the Bohr model and quantum mechanics
4Evidence only for the nucleus
- Evidence only for the nucleus the experiment did not prove the existence of protons and neutrons
Section 7 of 9More from the specification
Rutherford's Alpha Scattering Experiment
- Directing alpha particles at a thin gold foil revealed that most passed through undeflected while a tiny fraction scattered through large angles, proving that the atomic nucleus is small, dense,
- and positively charged.
Atomic Energy Levels
- Electrons in an atom exist in discrete, quantized energy levels;
- bound electrons cannot possess intermediate energies between these allowed quantum states.
Line Emission Spectra of Hydrogen
- When excited atomic electrons make a transition from a higher energy level to a lower level, photons of discrete wavelengths are emitted,
- producing characteristic spectral emission lines.
Photon Energy Equation
- The energy of each emitted photon equals the difference between the two energy levels: E = E₂ - E₁ = hf = hc / λ,
- where h is Planck's constant and c is the speed of light.
Photon
- A quantum of electromagnetic energy, E = hf
Wavelength
- Distance between a point on one wave and the same point on the next wave
Energy level
- A discrete energy an electron in an atom can have
Photon energy
- E = hf = hc/λ, the energy carried by one photon.
Emission spectrum
- The set of discrete wavelengths emitted by excited atoms of an element.
Spectral lines
- Dark or bright lines in a spectrum at wavelengths characteristic of elements.
Nuclear notation
- Symbol showing mass number and atomic number.
Subatomic particle
- A particle smaller than an atom, e.g. the electron.
∆E
∆E hf = E2 − E1
What the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10−34 J s) · f = frequency (Hz)
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Alpha particle | Helium nucleus (2 protons, 2 neutrons), charge +2e. |
| Nuclear model | Atom with a tiny dense positive nucleus surrounded by electrons. |
| Plum pudding model | Earlier model with positive charge spread through the atom. |
| Impact parameter | Perpendicular distance of the undeflected path from the nucleus. |
| Back-scattering | Deflection of an alpha particle through close to 180°. |
Section 9 of 9Exam technique
1
Saying alpha particles are deflected by electrons — electrons are far too light.
2
Claiming the nucleus contains all of the atom's mass — it contains almost all, more than 99.9%.
3
Thinking most alpha particles bounce back — only about 1 in 10^{4} are scattered through large angles.
4
Forgetting the vacuum or the thin foil as experimental requirements and their reasons.
5
Saying the experiment proved the existence of protons and neutrons — it showed only the nucleus.
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