P12: Nuclear Model and Isotopes
The development of the nuclear model of the atom, subatomic particles, isotopes, and an introduction to radioactive decay and background radiation.
Development of the Nuclear Model
Our understanding of atomic structure has changed over time as new evidence from experiments was discovered. Each new model refined the previous one.
Before the Nuclear Model
Before the discovery of the electron, atoms were thought to be tiny, indivisible spheres. In 1897, J.J. Thomson discovered the electron and proposed the plum pudding model.
The Plum Pudding Model
Thomson's model suggested that an atom was a ball of positive charge with electrons embedded within it, like plums in a pudding. The overall charge of the atom was neutral because the positive charge was balanced by the negative electrons.
Rutherford's Scattering Experiment (1911)
Ernest Rutherford, along with Hans Geiger and Ernest Marsden, conducted the famous alpha particle scattering experiment (also called the gold foil experiment).
They fired positively charged alpha particles at a thin sheet of gold foil. Most alpha particles passed straight through, but some were deflected and a very few bounced back towards the source.
The results led to three key conclusions:
- Most passed through β the atom is mostly empty space
- Some were deflected β the nucleus has a positive charge (like charges repel)
- Very few bounced back β the nucleus is very small and contains most of the atom's mass
This led Rutherford to propose the nuclear model: a tiny, dense, positively charged nucleus at the centre with electrons orbiting around it.
Later Developments
- 1913 β Niels Bohr proposed that electrons orbit the nucleus in fixed energy levels (shells), not at random distances
- 1932 β James Chadwick discovered the neutron, explaining why nuclei were heavier than expected from protons alone
| Scientist | Year | Model / Discovery | Key Feature |
|---|---|---|---|
| Dalton | 1803 | Solid sphere model | Atoms are tiny indivisible spheres |
| Thomson | 1897 | Plum pudding model | Positive ball with embedded electrons |
| Rutherford | 1911 | Nuclear model | Tiny positive nucleus, electrons orbit |
| Bohr | 1913 | Bohr model | Electrons in fixed energy levels |
| Chadwick | 1932 | Discovery of neutron | Nucleus contains protons and neutrons |
Subatomic Particles
Atoms are made up of three subatomic particles: protons, neutrons, and electrons. Protons and neutrons form the nucleus; electrons orbit the nucleus in shells.
| Particle | Relative Charge | Relative Mass | Location |
|---|---|---|---|
| Proton | +1 | 1 | Nucleus |
| Neutron | 0 | 1 | Nucleus |
| Electron | β1 | β 0.0005 (negligible) | Orbiting nucleus in shells |
In a neutral atom, the number of protons equals the number of electrons. The total positive charge from protons balances the total negative charge from electrons.
Charge of a nucleus = number of protons Γ (+1) = proton number
Mass of a nucleus β number of protons + number of neutrons
Atomic Number and Mass Number
The atomic number (proton number, Z) is the number of protons in the nucleus. It identifies the element. The mass number (A) is the total number of protons and neutrons in the nucleus.
Mass number (A) = number of protons + number of neutrons
Number of neutrons = mass number β atomic number
In a neutral atom: number of electrons = number of protons
Worked Example: Sodium
Sodium has atomic number 11 and mass number 23.
- Number of protons = 11
- Number of electrons = 11 (neutral atom)
- Number of neutrons = 23 β 11 = 12
Sodium is written as 11Na23 or using notation: 2311Na
Worked Example: Carbon
Carbon has atomic number 6 and mass number 12.
- Number of protons = 6
- Number of electrons = 6
- Number of neutrons = 12 β 6 = 6
Carbon notation: 126C
Isotopes
Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. They have the same atomic number but different mass numbers.
Because isotopes have the same electron arrangement, they have the same chemical properties. However, their physical properties (such as density and mass) may differ.
Carbon Isotopes
- Carbon-12 (126C): 6 protons, 6 neutrons, 6 electrons β the most common isotope
- Carbon-13 (136C): 6 protons, 7 neutrons, 6 electrons
- Carbon-14 (146C): 6 protons, 8 neutrons, 6 electrons β radioactive (used in radiocarbon dating)
All three have the same atomic number (6) but different mass numbers (12, 13, 14).
Hydrogen Isotopes
- Protium (11H): 1 proton, 0 neutrons β most common
- Deuterium (21H): 1 proton, 1 neutron β used in heavy water
- Tritium (31H): 1 proton, 2 neutrons β radioactive
Isotopes always have the same number of protons (same element, same atomic number) but a different number of neutrons (different mass number). Remember: chemical properties depend on electrons, not neutrons.
Radioactive Decay β Overview
Some isotopes have unstable nuclei. When a nucleus is unstable, it decays by emitting radiation to become more stable. This process is called radioactive decay and happens randomly β you cannot predict when a particular nucleus will decay.
There are three main types of nuclear radiation:
- Alpha (Ξ±) β a helium nucleus (2 protons + 2 neutrons)
- Beta (Ξ²) β a high-speed electron emitted from the nucleus
- Gamma (Ξ³) β electromagnetic radiation from the nucleus
Radioactive decay is a random process. It is not affected by physical conditions such as temperature, pressure, or chemical bonding. Only nuclear processes can change the rate of decay.
When a nucleus decays, the atomic number and/or mass number may change, forming a new element. This is called transmutation.
Background Radiation
Background radiation is the low-level ionising radiation that is always present around us. It comes from both natural and artificial sources.
Natural Sources
- Cosmic rays β high-energy particles from space, partly blocked by the atmosphere
- Rocks and soil β some rocks (e.g. granite) contain radioactive uranium and thorium
- Radon gas β produced by the decay of uranium in rocks; can accumulate in buildings; the largest source of background radiation
- Food and drink β some foods (e.g. bananas) contain small amounts of radioactive potassium-40
- Living things β all organisms contain trace amounts of carbon-14 and potassium-40
Artificial (Human-Made) Sources
- Medical sources β X-rays, CT scans, radiotherapy
- Nuclear power β waste from nuclear power stations
- Nuclear weapons testing β fallout from past atmospheric tests
- Industrial sources β radioactive sources used in industry
| Source | Type | Approximate % of Background Radiation |
|---|---|---|
| Radon gas | Natural | ~50% |
| Medical | Artificial | ~15% |
| Food and drink | Natural | ~11% |
| Cosmic rays | Natural | ~10% |
| Rocks and soil | Natural | ~8% |
| Other (nuclear, industrial) | Artificial | ~1% |
Radon gas is the single largest source of background radiation in the UK. When asked about background radiation, always mention both natural and artificial sources and state that radon gas is the biggest contributor.
Measuring Radiation
Radiation can be detected using a Geiger-MΓΌller (GM) tube connected to a counter. The count rate (number of decays per second or per minute) measures the activity of a radioactive source.
When measuring radiation from a source, you should always first measure and subtract the background count rate (with no source present) to get the corrected count rate.
Corrected count rate = measured count rate β background count rate
Worked Example: Correcting for Background
A student measures 245 counts per minute with a radioactive source present, and 15 counts per minute without the source (background).
Corrected count rate = 245 β 15 = 230 counts per minute
Practice Questions
1. Describe how the results of Rutherford's scattering experiment led to the nuclear model of the atom. [4 marks]
Most alpha particles passed straight through the gold foil, showing that the atom is mostly empty space. Some alpha particles were deflected, showing that the nucleus has a positive charge (like charges repel). A very small number bounced back, showing that the nucleus is very small and contains most of the atom's mass. This led to the nuclear model with a tiny, dense, positive nucleus surrounded by electrons.
2. An atom of chlorine has atomic number 17 and mass number 35. Calculate the number of protons, neutrons, and electrons in a neutral atom of chlorine. [3 marks]
Protons = 17 (equal to atomic number). Neutrons = 35 β 17 = 18. Electrons = 17 (same as protons in a neutral atom).
3. Explain what isotopes are and why they have identical chemical properties. [3 marks]
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. They have identical chemical properties because chemical properties depend on the electron arrangement, and isotopes have the same number of electrons (same atomic number means same proton number, which equals electron number in a neutral atom). The different number of neutrons does not affect chemical behaviour.
4. Uranium-235 has 92 protons. Calculate the number of neutrons in uranium-235. [1 mark]
Number of neutrons = 235 β 92 = 143.
5. State three natural sources of background radiation and identify the largest source. [4 marks]
Three natural sources: radon gas, cosmic rays, and radioactive rocks/soil (or food and drink). The largest source of background radiation is radon gas, which accounts for approximately 50% of background radiation exposure.
Maths Skills
Calculating Subatomic Particles from Atomic and Mass Numbers
Given the atomic number (Z) and mass number (A), you can determine the composition of any atom:
- Number of protons = Z (atomic number)
- Number of electrons = Z (in a neutral atom)
- Number of neutrons = A − Z (mass number minus atomic number)
Worked Example
An atom of titanium has atomic number 22 and mass number 48. How many protons, neutrons and electrons does it contain?
Protons = 22, Electrons = 22, Neutrons = 48 − 22 = 26
Calculating Relative Atomic Mass from Isotope Abundances
The relative atomic mass (Ar) is a weighted average of all naturally occurring isotopes:
Ar = (fractional abundance1 × mass1) + (fractional abundance2 × mass2) + ...
Worked Example
Chlorine has two isotopes: 35Cl (75% abundance) and 37Cl (25% abundance). Calculate the relative atomic mass.
Ar = (0.75 × 35) + (0.25 × 37) = 26.25 + 9.25 = 35.5
This is why chlorine's relative atomic mass on the periodic table is 35.5, not a whole number.
Worked Example
Boron has two isotopes: 10B (20% abundance) and 11B (80% abundance). Calculate Ar.
Ar = (0.20 × 10) + (0.80 × 11) = 2.0 + 8.8 = 10.8
Common Misconceptions
Isotopes and Protons
Isotopes have different numbers of protons. Isotopes of the same element always have the same number of protons (same atomic number). What differs is the number of neutrons, giving them different mass numbers. Changing the number of protons would make it a different element entirely.
Why Atoms Are Mostly Empty Space
The atom is mostly empty space because electrons are very small. The atom is mostly empty space because the nucleus is extremely tiny compared to the overall size of the atom. If an atom were the size of a football stadium, the nucleus would be the size of a pea at the centre. The electrons occupy the space around it but the vast majority of the atom's volume is empty.
6-Mark Extended Question
Describe how and why our model of the atom has changed from Dalton's solid sphere to the nuclear model. Include the evidence that led to each change. [6 marks]
Dalton proposed the solid sphere model, suggesting atoms were tiny indivisible spheres (1). Thomson discovered the electron in 1897, showing atoms contained smaller negatively charged particles, so he proposed the plum pudding model — a ball of positive charge with electrons embedded within it (1). Rutherford's alpha scattering experiment in 1911 tested this: most alpha particles passed straight through gold foil, showing the atom is mostly empty space (1). Some were deflected, showing the nucleus is positively charged (1). A very few bounced back, showing the nucleus is tiny but contains most of the mass (1). This led to the nuclear model with a small dense positive nucleus and orbiting electrons. Bohr later refined this by proposing electrons orbit in fixed energy levels, and Chadwick discovered the neutron in 1932, completing the modern picture (1).
AO3: Analyse and Evaluate
In Rutherford's scattering experiment, the following observations were made:
- Out of every 10 000 alpha particles fired at the gold foil, about 9998 passed straight through
- About 2 were deflected by more than 90°
- None were reflected directly back at the source
(a) Explain what each observation tells us about the structure of the atom. (b) If the experiment were repeated with aluminium foil instead of gold (aluminium has fewer protons per nucleus), how would you expect the results to differ and why?
Evaluation
(a) The vast majority passing through shows the atom is mostly empty space. The few large-angle deflections show the nucleus is very small (rare to hit it) but has a large positive charge (strong repulsion when an alpha particle does approach it). No particles reflecting directly back is consistent with the nuclear model — alpha particles are deflected, not reflected like a ball off a wall.
(b) With aluminium (fewer protons, smaller nuclear charge), fewer alpha particles would be significantly deflected because the repulsive force between the alpha particle and the smaller positive nucleus would be weaker. Also, aluminium is a lighter element so the nucleus would be less effective at deflecting the relatively massive alpha particles.
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