Atomic structure

Physics· Unit 11: Particle Physics, Topic 1· 15 min read

1. 1. Rutherford Scattering and the Nuclear Model★★☆☆☆⏱ 5 min

Before Rutherford's famous experiment, the accepted atomic model was J.J. Thomson's plum pudding model, which described negative electrons embedded evenly in a uniform sphere of positive charge.

📘 Definition

Plum Pudding Model

Early atomic model where negative electrons are distributed evenly through a uniform sphere of positive charge

Rutherford, Geiger and Marsden tested this model by firing positively charged alpha particles at thin gold foil. Most passed through undeflected, but a tiny fraction deflected through angles >90°, which could not be explained by the plum pudding model.

📐 Worked Example

State three conclusions from Rutherford's experiment, linking each to the corresponding observation.

1
Observation 1: Most alpha particles pass straight through the foil. Conclusion 1:
2
Most of the atom is empty space, with mass concentrated in a small central region.
3
Observation 2: Some alpha particles are deflected through small angles. Conclusion 2:
4
The central nucleus is positively charged, and repels positively charged alpha particles.
5
Observation 3: Very few alpha particles deflect through angles >90°. Conclusion 3:
6
Almost all the mass of the atom is concentrated in a very small, dense central nucleus.

Exam tip:

Never mix up observations and conclusions — examiners always test this distinction.

2. 2. Nuclear Notation and Key Terms★☆☆☆☆⏱ 3 min

All atomic nuclei are made of nucleons (protons and neutrons). We use standard notation to describe any nuclide, with two key numbers: proton number (Z) and nucleon number (A).

📘 Definition

Nuclide

^A_Z \text{X}

A specific type of atom defined by its proton and nucleon count

Example:

Carbon-12 is written $_{16}^{12} C$

Proton number (Z): Number of protons in the nucleus, equal to the positive charge of the nucleus
Nucleon number (A): Total number of protons + neutrons in the nucleus
Neutron number: $N = A - Z$ , number of neutrons in the nucleus
Isotope: Nuclides of the same element (same Z) with different N/A

📐 Worked Example

How many protons, neutrons and electrons are in a neutral $_{192}^{238} U$ atom?

1
Proton number $Z = 92$ , so there are 92 protons.
2
For a neutral atom, electron count equals proton count, so 92 electrons.
3
Calculate neutron number:
4
$N = A - Z = 238 - 92 = 146$
5
Final answer: 92 protons, 92 electrons, 146 neutrons.

3. 3. Nuclear Size and Density★★★☆☆⏱ 4 min

Experiments confirm that nuclear radius follows a simple proportional relationship with nucleon number:

R = R_0 A^{1/3}

Where $R_{0} \approx 1.2 \times 1 0^{- 15} m = 1.2 fm$ . This relationship leads to a very useful property: all nuclei have approximately the same density, regardless of size.

📐 Worked Example

Calculate the radius of an oxygen-16 nucleus, given $R_{0} = 1.2$ fm.

1
Oxygen-16 has nucleon number $A = 16$ .
2
Substitute into the formula:
3
$R = 1.2 \times (16)^{1/3}$
4
Calculate $(16)^{1/3} \approx 2.5198$
5
Final result: $R \approx 1.2 \times 2.52 = 3.02$ fm, or $3.02 \times 1 0^{- 15}$ m.

4. 4. Isotope Properties★★☆☆☆⏱ 3 min

Isotopes of the same element have identical chemical properties, but different physical and nuclear properties. This is because chemical reactions depend on the number and arrangement of electrons, which is determined by proton number, which is the same for all isotopes of an element.

Differences in neutron number change the mass and nuclear stability of isotopes, leading to different physical properties (e.g. density, boiling point) and nuclear behaviour (e.g. radioactivity).

📐 Worked Example

State one similarity and one difference between $_{8}^{16} O$ and $_{8}^{18} O$ .

1
Similarity: Both have 8 protons and 8 electrons when neutral, so they have identical chemical properties.
2
Difference: $_{8}^{16} O$ has 8 neutrons, $_{8}^{18} O$ has 10 neutrons. They have different masses and different nuclear stabilities.

5. Common Pitfalls

Wrong move:

Confusing Rutherford scattering observations with conclusions

Why:

Students often list what was seen instead of what was deduced from the results

Correct move:

Always link each observation directly to its corresponding conclusion in exam answers

Wrong move:

Calculating neutron number as $Z - A$ instead of $A - Z$

Why:

Mixing up the order of proton and nucleon number in the subtraction

Correct move:

Remember: neutrons = total nucleons minus protons = $A - Z$

Wrong move:

Claiming isotopes have different chemical properties

Why:

Confusing nuclear/physical properties with chemical properties that depend on electrons

Correct move:

Isotopes of the same element have identical chemical properties, only differing in mass and nuclear stability

Wrong move:

Forgetting electron count equals Z for neutral atoms

Why:

Assuming all atoms are ions without checking the question

Correct move:

Only adjust electron count for charged ions; for neutral atoms, electrons = Z

6. Quick Reference Cheatsheet

Term	Notation/Formula	Meaning
Proton Number	$Z$	Number of protons in nucleus
Nucleon Number	$A$	Total number of protons + neutrons
Neutron Number	$N = A - Z$	Number of neutrons in nucleus
Nuclide Notation	$_{Z}^{A} X$	Standard notation for nuclides
Nuclear Radius	$R = R_{0} A^{1/3}$	$R_{0} = 1.2$ fm
Isotopes	Same $Z$ , different $A$	Same element, different neutron count

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · 1
MCQ on Rutherford scattering conclusions
2023 · 2
Calculation of nuclear radius
2021 · 1
Isotope identification and properties

What's Next

Understanding atomic structure and nuclear properties is the core foundation for all further topics in CIE A-Level AS particle and nuclear physics. Now that you have mastered the basic structure, nuclide notation and key experimental evidence from Rutherford scattering, you are ready to explore the composition of nucleons and the classification of fundamental particles. This knowledge will also be critical for later topics including radioactivity, nuclear fission and fusion, where you will apply your understanding of nuclide notation to balance decay equations and calculate key nuclear properties.