Atomic structure

IB Physics SL· 45 min read

1. Basic Atomic Structure★★☆☆☆⏱ 10 min

📘 Definition

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 $1 0^{- 15} m$ in diameter, while the entire atom has a diameter of roughly $1 0^{- 10} m$ . 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 $1 \times 1 0^{- 15}$ of the total volume.

2. Nuclear Notation and Nuclide Properties★★☆☆☆⏱ 15 min

📘 Definition

Nuclide Notation

^A_Z X

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.

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 $_{92}^{238} U$ 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
$N = 238 - 92 = 146$

✓ Quick check

Test your understanding of notation:

How many neutrons are in $_{17}^{37} Cl$ ?
- 17
- 20
- 37
- 54
Reveal answer
20 —
Correct! $N = A - Z = 37 - 17 = 20$ .

3. Isotopes and Specific Charge Calculations★★★☆☆⏱ 20 min

📘 Definition

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: $_{1}^{1} H$ (protium), $_{1}^{2} H$ (deuterium), $_{1}^{3} H$ (tritium)

📘 Definition

Specific Charge

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

Proton mass and neutron mass are approximately equal ( $\approx 1.67 \times 1 0^{- 27} kg$ ), while the proton charge is $+ 1.60 \times 1 0^{- 19} C$ 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 $_{8}^{16} O$ 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
$\text{Specific charge} = \frac{1.28 \times 10^{-18}}{2.672 \times 10^{-26}} \approx 4.79 \times 10^7\ \text{C kg}^{-1}$

4. Common Pitfalls

Wrong move:

Counting electrons equal to $A$ (mass number) instead of $Z$ (atomic number) for neutral atoms

Why:

Confusion between the meaning of mass number and atomic number

Correct move:

Always use $Z$ for proton and electron count in neutral atoms, calculate neutron count as $A - Z$

Wrong move:

Including electron mass when calculating specific charge of a nucleus

Why:

Misinterpreting whether the question asks for the specific charge of the whole atom or the nucleus

Correct move:

Only include mass of protons and neutrons for nuclear specific charge calculations

Wrong move:

Claiming isotopes of the same element have different chemical properties

Why:

Confusing chemical properties (determined by electrons) with nuclear properties

Correct move:

Isotopes have identical chemical properties and different nuclear properties

Wrong move:

Writing nuclear notation with $A$ at the bottom and $Z$ at the top

Why:

Mixing up the position of mass and atomic number

Correct move:

Remember: Always Atop = mass number A, Z at the bottom

Wrong move:

Reporting negative specific charge for negative ions/nuclei

Why:

Forgetting specific charge uses magnitude of charge by definition

Correct move:

Specific charge is always reported as a positive value, regardless of overall charge sign

5. Quick Reference 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	$_{Z}^{A} X$	$A$ (mass) = top, $Z$ (atomic) = bottom

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
Isotope identification multiple choice
2023 · 2
Calculate specific charge of nucleus

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
→Nuclear reactions