P11: Nuclear Model and Isotopes
Development of the nuclear model and isotopes
📋 Key Definitions
Atomic number (proton number): The number of protons in the nucleus of an atom. This identifies the element.
Mass number: The total number of protons and neutrons in the nucleus of an atom.
Isotopes: Atoms of the same element that have the same number of protons but a different number of neutrons. They have the same atomic number but different mass numbers.
Radioactivity: The process by which an unstable nucleus emits radiation to become more stable.
🔬 Discovery of the Nucleus — Rutherford's Alpha Scattering
Before Rutherford, the accepted model was the plum pudding model (Thomson), which suggested that atoms were spheres of positive charge with electrons embedded in them.
In 1909, Rutherford, Geiger and Marsden fired alpha particles at thin gold foil. The results changed our understanding of the atom:
| Observation | What most particles did | Conclusion |
|---|---|---|
| Most alpha particles went straight through | Passed through with no deflection | Atom is mostly empty space |
| Some alpha particles were deflected | Deflected at large angles | Nucleus has a positive charge (repelled the positive alpha particles) |
| A few alpha particles bounced back | Deflected back towards the source | Nucleus is very small, dense and contains most of the atom's mass |
Rutherford's conclusions: The atom has a tiny, positive, dense nucleus at its centre. Most of the atom is empty space. Electrons orbit the nucleus at a distance.
Worked Example 1: Explaining alpha scattering
Explain why a few alpha particles were deflected back towards the source in Rutherford's experiment.
The alpha particles (which are positive) approached the nucleus head-on. Since the nucleus is also positive and very dense, the repulsive force was strong enough to push the alpha particles back towards the source. This shows the nucleus is small (very few particles hit it), positive (repels positive alphas), and dense/massive (can deflect heavy alpha particles).
⚛️ Atomic Structure
| Subatomic particle | Relative mass | Relative charge | Location |
|---|---|---|---|
| Proton | 1 | +1 | Nucleus |
| Neutron | 1 | 0 | Nucleus |
| Electron | Very small (≈ 0.0005) | −1 | Orbiting the nucleus |
Key facts: The number of protons = number of electrons in a neutral atom. Proton number = atomic number. Mass number = protons + neutrons. To find neutrons: neutrons = mass number − atomic number.
Number of neutrons = mass number − atomic number
Worked Example 2: Calculating neutrons
Carbon has an atomic number of 6 and a mass number of 12. How many protons, neutrons and electrons does a carbon-12 atom have?
Protons = atomic number = 6
Electrons = protons = 6 (neutral atom)
Neutrons = mass number − atomic number = 12 − 6 = 6
Worked Example 3: A larger atom
Uranium has atomic number 92 and mass number 238. Calculate the number of neutrons.
Neutrons = 238 − 92 = 146
🔁 Isotopes
Isotopes are atoms of the same element (same number of protons) with a different number of neutrons. They have the same atomic number but different mass numbers.
Isotopes have the same chemical properties (because they have the same number of electrons and the same electron configuration) but different physical properties (different mass, different density).
Worked Example 4: Isotopes of hydrogen
Hydrogen-1 (protium): 1 proton, 0 neutrons, mass number = 1
Hydrogen-2 (deuterium): 1 proton, 1 neutron, mass number = 2
Hydrogen-3 (tritium): 1 proton, 2 neutrons, mass number = 3
All three are isotopes of hydrogen — same atomic number (1), different mass numbers.
Worked Example 5: Isotopes of carbon
Carbon-12: 6 protons, 6 neutrons (mass number 12)
Carbon-14: 6 protons, 8 neutrons (mass number 14)
Both are isotopes of carbon. Carbon-14 is radioactive and is used in carbon dating.
☢️ Radioactivity and Background Radiation
Some isotopes have unstable nuclei. These nuclei decay by emitting radiation to become more stable. This process is random — you cannot predict when a particular nucleus will decay.
Types of nuclear radiation:
- Alpha (α): 2 protons + 2 neutrons (helium nucleus)
- Beta (β): a fast-moving electron
- Gamma (γ): an electromagnetic wave
- Neutron: a neutron emitted from the nucleus
Background radiation is the low-level radiation that is always present around us. Sources include:
| Source | Description |
|---|---|
| Cosmic rays | Radiation from space (from the Sun and other stars) |
| Rocks and soil | Naturally radioactive minerals in the Earth's crust (e.g. uranium, thorium) |
| Radon gas | Radioactive gas released from rocks — the largest source of background radiation in the UK |
| Food and drink | Naturally radioactive isotopes (e.g. potassium-40 in bananas) |
| Medical | X-rays, CT scans, radiotherapy (artificial source) |
| Nuclear industry | Nuclear power stations and waste (very small contribution) |
Background radiation is mostly natural (about 85% from natural sources like radon gas, cosmic rays and rocks). Only about 15% comes from artificial sources like medical procedures.
❓ Practice Questions
Q1: Foundation Describe the results of Rutherford's alpha scattering experiment and what each result tells us about the structure of the atom.
Q2: Foundation An atom has 26 protons and 30 neutrons. State its atomic number and mass number.
Q3: Higher Explain what isotopes are, using carbon-12 and carbon-14 as examples.
Q4: Higher Chlorine has two isotopes: Cl-35 (75%) and Cl-37 (25%). Explain why they have the same chemical properties but different physical properties.
Q5: Foundation List four sources of background radiation and identify which is the largest natural source in the UK.
Q6: Higher Uranium-235 has atomic number 92. Calculate the number of protons, neutrons and electrons in a neutral U-235 atom.
✅ Answers
- Most alpha particles went straight through → the atom is mostly empty space. Some were deflected → the nucleus is positively charged. A few bounced back → the nucleus is small, dense and contains most of the mass.
- Atomic number = 26 (number of protons). Mass number = 26 + 30 = 56 (protons + neutrons). This is iron-56.
- Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons. Carbon-12 has 6 protons and 6 neutrons. Carbon-14 has 6 protons and 8 neutrons. They are both carbon (atomic number 6) but have different mass numbers (12 and 14).
- Same chemical properties because they have the same number of electrons (17) and the same electron configuration. Different physical properties because they have different masses (Cl-35 has 18 neutrons, Cl-37 has 20 neutrons).
- Four sources: radon gas, cosmic rays, rocks and soil, food and drink (also accept medical, nuclear industry). Radon gas is the largest natural source in the UK.
- Protons = 92, Neutrons = 235 − 92 = 143, Electrons = 92 (neutral atom).
🎯 Exam Tips
- Make sure you can explain all three observations from Rutherford's experiment and the conclusion from each one
- When calculating neutrons, always do mass number minus atomic number — don't confuse the two
- Isotopes must have the same proton number but different neutron numbers — both conditions are needed
- Remember: chemical properties depend on electrons, physical properties depend on mass — this explains why isotopes have the same chemistry but different physics
- Background radiation is mostly natural — don't forget radon gas as the biggest UK source
- The plum pudding model was before Rutherford — the nuclear model replaced it based on the scattering evidence
🔢 Maths Skills
Mathematical Skills
Calculate the number of neutrons using: neutrons = mass number − atomic number. You may also need to calculate the relative atomic mass from isotope abundances using: Ar = (mass₁ × %₁ + mass₂ × %₂) / 100.
Maths Example
Chlorine has two isotopes: Cl-35 (75%) and Cl-37 (25%). Calculate the relative atomic mass: Ar = (35 × 75 + 37 × 25) / 100 = (2625 + 925) / 100 = 3550 / 100 = 35.5.
⚠️ Common Misconceptions
Watch Out!
1. Wrong: Isotopes have different chemical properties because they have different numbers of neutrons. Correct: Isotopes have the SAME chemical properties because chemical behaviour depends on electron arrangement, which is determined by proton number.
2. Wrong: Rutherford's experiment proved the plum pudding model was correct. Correct: Rutherford's experiment DISPROVED the plum pudding model — the results showed the atom has a small, dense, positive nucleus, not a diffuse positive charge.
3. Wrong: Neutrons have no mass because they have no charge. Correct: Neutrons have a relative mass of 1 (the same as protons) — they have zero charge but do have mass.
✍️ 6-Mark Question
Extended Answer
6 marks: Describe the alpha scattering experiment and explain how the results led to the nuclear model of the atom, replacing the plum pudding model.
Rutherford, Geiger and Marsden fired alpha particles at thin gold foil. Most alpha particles passed straight through, which showed that the atom is mostly empty space. Some alpha particles were deflected at large angles, which showed the nucleus has a positive charge because it repelled the positive alpha particles. A very few alpha particles bounced back towards the source, which showed the nucleus is very small, dense and contains most of the atom's mass. These results could not be explained by the plum pudding model, which predicted that all alpha particles would pass through with only small deflections. The new nuclear model — a tiny positive nucleus surrounded by electrons in mostly empty space — was developed to explain these observations.
Mark scheme: 1 mark for most passed through → empty space; 1 mark for some deflected → positive nucleus; 1 mark for few bounced back → small dense nucleus with most mass; 1 mark for plum pudding model predicted no large deflections; 1 mark for new model with tiny nucleus + electrons; 1 mark for clear link between observation and conclusion. (6 marks total)
📊 AO3: Analyse & Evaluate
Analysis and Evaluation
A student looks up data for three isotopes of uranium: U-234 (0.005% abundance), U-235 (0.720% abundance), U-238 (99.275% abundance). All have atomic number 92.
(a) Calculate the number of neutrons in U-235 and U-238.
(b) Explain why U-235 and U-238 have the same chemical properties despite having different mass numbers.
(c) U-235 is used as fuel in nuclear reactors but U-238 is not. A process called enrichment increases the percentage of U-235. Evaluate why enrichment is necessary given the natural abundance data.
Answers: (a) U-235: neutrons = 235 − 92 = 143. U-238: neutrons = 238 − 92 = 146. (b) They have the same number of protons (92) and therefore the same number of electrons (92), giving the same electron configuration. Chemical properties depend on electrons, not neutrons. (c) Natural uranium is 99.3% U-238 and only 0.7% U-235. U-235 is fissile (can undergo fission with slow neutrons) but U-238 is not. With such a low natural percentage, the chain reaction cannot be sustained because too few U-235 nuclei are present to absorb neutrons and keep the reaction going. Enrichment to 3–5% U-235 is needed to ensure enough fission events occur to maintain a chain reaction in a reactor.
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