# Atomic structure

> IB Physics SL · Nuclear and quantum physics
> Source: https://www.owlsprep.com/study/ib-physics-sl-u5-atomic-structure/

This subtopic covers the fundamental structure of the atom, key nuclear properties, standard notation, and core calculations that underpin all subsequent nuclear and quantum physics topics for IB SL.

**Prerequisites:** [Basic particle classification](https://www.owlsprep.com/study/ib-physics-sl-particles-fundamentals/)

## Learning objectives

- Describe the fundamental structure of the atom and nucleus
- Interpret standard nuclear notation for nuclides
- Distinguish between the properties of isotopes of the same element
- Calculate the specific charge of nuclei and nucleons

## Basic Atomic Structure

**Atom** — The smallest neutral unit of an element that retains all chemical properties of the element. It consists of a small, dense positively charged nucleus surrounded by a negatively charged electron cloud.

*Example:* A neutral carbon atom contains 6 protons and 6 electrons.

Most of the atom is empty space. The nucleus is approximately $10^{-15}\ \text{m}$ in diameter, while the entire atom has a diameter of roughly $10^{-10}\ \text{m}$. The nucleus contains two types of nucleon: positively charged protons and neutral neutrons.

**Worked example:** Estimate the ratio of the volume of a whole atom to the volume of its nucleus, assuming both are spherical.

1. Use standard approximate radii:
2. $$r_{\text{atom}} \approx 10^{-10}\ \text{m}, \quad r_{\text{nucleus}} \approx 10^{-15}\ \text{m}$$
3. Volume of a sphere is proportional to $r^3$, so the ratio simplifies to:
4. $$\frac{V_{\text{atom}}}{V_{\text{nucleus}}} = \left(\frac{r_{\text{atom}}}{r_{\text{nucleus}}}\right)^3$$
5. Substitute values to get the result:
6. $$\left(\frac{10^{-10}}{10^{-15}}\right)^3 = (10^5)^3 = 10^{15}$$
7. This confirms the atom is mostly empty space, with the nucleus taking up just $1 \times 10^{-15}$ of the total volume.

## Nuclear Notation and Nuclide Properties

**Nuclide Notation** — Standard notation for nuclides where: $A$ = total number of nucleons (mass number), $Z$ = number of protons (atomic number), and $X$ is the chemical symbol of the element.

*Notation:* ^A_Z X

The number of neutrons in any nuclide is calculated as $N = A - Z$. The proton number $Z$ defines the element: all atoms of the same element will always have the same value of $Z$. For neutral atoms, the number of negatively charged electrons equals the number of positively charged protons, giving a net charge of zero.

**Worked example:** State the number of protons, neutrons and electrons in a neutral $^{238}_{92}\text{U}$ atom.

1. Extract $Z$ and $A$ from notation: $Z = 92$, $A = 238$
2. Number of protons = $Z$ = 92. For a neutral atom, number of electrons equals number of protons, so electrons = 92.
3. Calculate number of neutrons as $A - Z$:
4. $$N = 238 - 92 = 146$$

**Check your understanding**

Test your understanding of notation:

1. How many neutrons are in $^{37}_{17}\text{Cl}$?

   - 17
   - 20
   - 37
   - 54

   *Why:* Correct! $N = A-Z = 37 - 17 = 20$.

## Isotopes and Specific Charge Calculations

**Isotopes** — Nuclides of the same element (same $Z$) that have different mass numbers $A$, so different numbers of neutrons. Isotopes have identical chemical properties (determined by electron arrangement) but different nuclear properties.

*Example:* Hydrogen has 3 naturally occurring isotopes: $^1_1\text{H}$ (protium), $^2_1\text{H}$ (deuterium), $^3_1\text{H}$ (tritium)

**Specific Charge** — The ratio of the magnitude of a particle's total charge to its total mass, usually quoted in units of $\text{C kg}^{-1}$ for nuclei.

Proton mass and neutron mass are approximately equal ($\approx 1.67 \times 10^{-27}\ \text{kg}$), while the proton charge is $+1.60 \times 10^{-19}\ \text{C}$ and neutrons have zero charge. When calculating specific charge for a nucleus, we only include the mass and charge of the nucleons, not the orbiting electrons.

**Worked example:** Calculate the specific charge of an $^{16}_{8}\text{O}$ nucleus. Give your answer to 3 significant figures.

1. Calculate total charge of the nucleus: $Z = 8$, so:
2. $$Q = 8e = 8 \times 1.60 \times 10^{-19} = 1.28 \times 10^{-18}\ \text{C}$$
3. Calculate total mass of the nucleus: $A = 16$, so:
4. $$M = 16 \times 1.67 \times 10^{-27} = 2.672 \times 10^{-26}\ \text{kg}$$
5. Calculate specific charge as $\frac{Q}{M}$:
6. $$\text{Specific charge} = \frac{1.28 \times 10^{-18}}{2.672 \times 10^{-26}} \approx 4.79 \times 10^7\ \text{C kg}^{-1}$$

## Common pitfalls

- **Wrong:** Counting electrons equal to $A$ (mass number) instead of $Z$ (atomic number) for neutral atoms
  - Why it fails: Confusion between the meaning of mass number and atomic number
  - Correct: Always use $Z$ for proton and electron count in neutral atoms, calculate neutron count as $A-Z$
- **Wrong:** Including electron mass when calculating specific charge of a nucleus
  - Why it fails: Misinterpreting whether the question asks for the specific charge of the whole atom or the nucleus
  - Correct: Only include mass of protons and neutrons for nuclear specific charge calculations
- **Wrong:** Claiming isotopes of the same element have different chemical properties
  - Why it fails: Confusing chemical properties (determined by electrons) with nuclear properties
  - Correct: Isotopes have identical chemical properties and different nuclear properties
- **Wrong:** Writing nuclear notation with $A$ at the bottom and $Z$ at the top
  - Why it fails: Mixing up the position of mass and atomic number
  - Correct: Remember: *A*lways *A*top = mass number A, Z at the bottom
- **Wrong:** Reporting negative specific charge for negative ions/nuclei
  - Why it fails: Forgetting specific charge uses magnitude of charge by definition
  - Correct: Specific charge is always reported as a positive value, regardless of overall charge sign

## Cheatsheet

| Property | Symbol/Rule | Notes |
| --- | --- | --- |
| Proton (atomic) number | $Z$ | Defines the element, equals number of protons |
| Nucleon (mass) number | $A$ | Total number of protons + neutrons |
| Number of neutrons | $N$ | $N = A - Z$ |
| Electrons in neutral atom | $e^-$ | $e^- = Z$ |
| Specific charge | $\frac{\|Q\|}{M}$ | Units: C kg⁻¹, only nucleons for nuclei |
| Isotopes | Same $Z$, different $A$ | Same chemical properties |
| Standard notation | $^A_Z X$ | $A$ (mass) = top, $Z$ (atomic) = bottom |

## What's next

Atomic structure is the foundational concept for all nuclear and quantum physics topics you will study in this unit. Mastery of nuclide notation and specific charge calculations is required for almost every subsequent nuclear topic, from radioactive decay to nuclear fission and fusion. Next, you will build on this core knowledge to learn how Rutherford's gold foil experiment confirmed the nuclear model of the atom, before moving on to study radioactive decay processes and nuclear reactions. The distinction between isotopes you learned here is also critical for understanding half-life and energy calculations in nuclear physics.

- [Radioactive decay](https://www.owlsprep.com/study/ib-physics-sl-u5-radioactive-decay/)
- [Nuclear reactions](https://www.owlsprep.com/study/ib-physics-sl-u5-nuclear-reactions/)

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