Structure 1.2 | The Nuclear Atom

📋 IB Content Statements (S1.2)

This topic covers the following syllabus points from the IB Chemistry 2025 guide:

S1.2.1: Atoms contain a positively charged, dense nucleus composed of protons and neutrons (nucleons). Negatively charged electrons occupy the space outside the nucleus.
S1.2.2: Isotopes are atoms of the same element with different numbers of neutrons.
S1.2.3: The relative atomic mass ($A_r$) of an element is the weighted mean of the masses of its isotopes relative to ¹²C.
S1.2.4: The number of protons (atomic number, $Z$) defines the element. The mass number ($A$) is the sum of protons and neutrons.

HL

HL Extensions

S1.2.5: Mass spectrometry is used to determine the relative atomic mass and the abundance of isotopes of an element.
S1.2.6: Ions are created in a mass spectrometer by bombardment with high-energy electrons.

🔹 Subatomic Particles

The atom consists of a small, dense nucleus (containing protons and neutrons) surrounded by electrons in energy levels (shells).

Particle	Relative Mass	Relative Charge	Location	Symbol
Proton	1	+1	Nucleus	$p^+$
Neutron	1	0	Nucleus	$n^0$
Electron	$\frac{1}{1840}$ (≈ 0)	−1	Energy levels (shells)	$e^-$

Historical models:

Dalton (1803): Atoms are solid, indivisible spheres.
Thomson (1897): "Plum pudding" — electrons embedded in positive dough. Discovered the electron.
Rutherford (1911): Gold foil experiment → most of the atom is empty space with a small, dense, positive nucleus.
Bohr (1913): Electrons orbit in fixed energy levels (shells).

Evolution of atomic models from Dalton to Bohr

🔢 Nuclear Notation

Notation: ${}_{Z}^{A}X$

$A$ = Mass number = protons + neutrons (top)
$Z$ = Atomic number = number of protons (bottom) — this defines the element

Calculating Subatomic Particles

Quantity	Formula	Example: ${}_{17}^{35}Cl$	Example: ${}_{17}^{37}Cl^-$
Protons	$Z$	17	17
Neutrons	$A - Z$	$35 - 17 = 18$	$37 - 17 = 20$
Electrons	$Z - \text{charge}$	17 (neutral atom)	$17 + 1 = 18$ (anion)

⚠️ Ions: For cations (+), subtract the charge from $Z$ to get electrons. For anions (−), add the magnitude of the charge. $Na^+$ has 10 electrons (11 − 1). $O^{2-}$ has 10 electrons (8 + 2).

⚛️ Isotopes & Relative Atomic Mass

📺 S1.2.2 — RAM Calculations with Isotope Abundance

📺 S1.2.2 — Physical Properties of Isotopes

Definition: Isotopes

Atoms of the same element (same number of protons / same $Z$) with different numbers of neutrons (different $A$).

Properties of Isotopes

Property Type	Same or Different?	Reason
Chemical properties	Same	Same number of electrons → same bonding and reactivity
Physical properties	Different	Different mass → different density, melting/boiling point, rate of diffusion
Radioactivity	May differ	Some isotopes are stable, others are radioactive (unstable nucleus)

Calculating Relative Atomic Mass ($A_r$)

$$A_r = \frac{(\text{mass}_1 \times \text{abundance}_1) + (\text{mass}_2 \times \text{abundance}_2)}{100}$$

Worked example: Chlorine has two isotopes: $^{35}Cl$ (75.8%) and $^{37}Cl$ (24.2%).

$A_r = \frac{(35 \times 75.8) + (37 \times 24.2)}{100} = \frac{2653 + 895.4}{100} = 35.48$

Why $A_r$ values on the periodic table aren't whole numbers: They are weighted averages of all naturally occurring isotopes. Chlorine's $A_r$ of 35.5 reflects that it has roughly 3 parts $^{35}Cl$ for every 1 part $^{37}Cl$.

🧪 Mass Spectrometry (HL)

📺 S1.2.3 — Mass Spectra of Isotopes (HL)

HL

The Mass Spectrometer

A mass spectrometer separates atoms or molecules based on their mass-to-charge ratio ($m/z$).

Five Stages of Mass Spectrometry

Stage	Process	Detail
1. Vaporization	Sample → gas phase	Heated to produce gaseous atoms/molecules
2. Ionization	Atoms → positive ions	High-energy electron bombardment removes an electron: $X(g) \rightarrow X^+(g) + e^-$
3. Acceleration	Ions accelerated	Electric field gives all ions the same kinetic energy
4. Deflection	Ions separated	Magnetic field deflects lighter ions more; heavier ions deflect less
5. Detection	Ions detected	Produces a mass spectrum: peaks at each $m/z$ value

Reading a Mass Spectrum

Number of peaks = number of isotopes
Position (x-axis) = mass-to-charge ratio ($m/z$)
Height (y-axis) = relative abundance (%)
Tallest peak = most abundant isotope

Interactive: Mass Spectrometry

Available

Explore mass spectra of different elements and calculate $A_r$ from spectral data.

→ Launch Simulation

🧪 Interactive Virtual Labs

Mass Spectrometry Explorer

Available

Explore mass spectra of different elements. Calculate relative atomic mass from abundance data.

→ Launch Simulation

🧠 Memory Aids & Mnemonics

🔤 Subatomic Particle Table

"PEN" → Proton, Electron, Neutron (+1, −1, 0)

The charges go +1, −1, 0 in alphabetical order of the first letter. P is positive, E is negative (think: e for electron, e for "elementary negative charge"), N is neutral.

🔤 Mass Number vs Atomic Number

"A is Above, Z is Below" (in nuclear notation ${}_{Z}^{A}X$)

$A$ (mass number) is the superscript (above). $Z$ (atomic number) is the subscript (below). $Z$ = protons = defines the element. $A$ = protons + neutrons.

🔤 Isotopes Definition

"Same Protons, Different Neutrons"

Isotopes have the same atomic number ($Z$) but different mass numbers ($A$). They are the same element because they have the same number of protons. Chemical properties are the same because they have the same number of electrons.

🔤 Mass Spectrometer Steps (HL)

"Very Intelligent Athletes Dodge Defenders"

Vaporization → Ionization → Acceleration → Deflection → Detection. Five stages in order.

🌍 Real-World Applications

🦴 Radiocarbon Dating (Carbon-14)

Context: How do archaeologists know a bone is 5,000 years old? They use the isotope Carbon-14.

Science: Living organisms constantly absorb $^{14}C$ from the atmosphere (via $CO_2$). When the organism dies, $^{14}C$ is no longer absorbed and begins to decay: $^{14}C \rightarrow ^{14}N + \beta^-$ with a half-life of 5,730 years. By measuring the ratio of $^{14}C$ to stable $^{12}C$ in a sample, scientists calculate the time since death. This works for samples up to ~50,000 years old.

Impact: Radiocarbon dating has revolutionized archaeology, geology, and climate science. It confirmed the age of the Dead Sea Scrolls and helped date the last Ice Age.

🏥 Medical Isotopes (Technetium-99m)

Context: Hospitals use radioactive isotopes to diagnose diseases without surgery. Over 40 million nuclear medicine procedures are performed worldwide each year.

Science: Technetium-99m ($^{99m}Tc$) is the most widely used medical isotope. It emits gamma rays (detected by cameras outside the body) and has a short half-life of just 6 hours — long enough to perform scans but short enough to minimize radiation exposure. It can be attached to different molecules to target specific organs (bones, heart, kidneys, brain).

Impact: Medical isotopes save millions of lives annually. Iodine-131 treats thyroid cancer by selectively destroying thyroid cells. PET scans use Fluorine-18 to detect cancerous tumors by tracking glucose metabolism.

🔬 Forensic Mass Spectrometry

Context: Mass spectrometry is used in drug testing, forensic investigations, and doping control at the Olympics.

Science: In a mass spectrometer, unknown substances are vaporized, ionized, and separated by mass. The resulting mass spectrum acts as a chemical fingerprint — each substance produces a unique pattern of peaks. By comparing the spectrum to a database, forensic scientists can identify drugs, poisons, explosives, or environmental pollutants in tiny quantities (parts per billion).

Impact: GC-MS (gas chromatography–mass spectrometry) is the "gold standard" for forensic drug testing. It was used to identify nerve agents in the Novichok poisoning cases and is routinely used in anti-doping tests at the Olympics.

⚠️ Common Mistakes & Exam Pitfalls

🚫 Mistakes Students Make in This Topic

Confusing mass number with relative atomic mass: Mass number ($A$) is always a whole number (protons + neutrons for one specific isotope). $A_r$ is a weighted average and usually has decimal places (e.g., Cl = 35.5).
Forgetting to adjust electrons for ions: $Fe^{3+}$ has 23 electrons (26 − 3), not 26. $S^{2-}$ has 18 electrons (16 + 2), not 16. Always check the charge!
Saying isotopes have different chemical properties: Isotopes have the same chemical properties because they have the same electron configuration. Only physical properties differ (mass, density, rate of diffusion).
Wrong formula for $A_r$ calculation: Don't just average the masses. You must use a weighted average: $A_r = \frac{\sum(\text{mass} \times \text{abundance})}{100}$. If one isotope is much more abundant, $A_r$ will be closer to that isotope's mass.
Confusing atomic number with mass number positions: $A$ (mass) is the superscript (top), $Z$ (atomic number) is the subscript (bottom). Many students reverse these.

📝 IB-Style Exam Questions

Question 1: Calculate the relative atomic mass of Boron given: Boron-10 (19.9%) and Boron-11 (80.1%). [2 marks]

Mark Scheme:

[1 mark] Calculation: $\frac{(10 \times 19.9) + (11 \times 80.1)}{100}$
[1 mark] Answer: 10.8

Question 2: State two physical properties that differ for isotopes of the same element. [2 marks]

Mark Scheme:

[1 mark] Mass / density
[1 mark] Boiling point / melting point / rate of diffusion

Question 3: Describe the purpose of the magnetic field in a mass spectrometer. [1 mark]

Mark Scheme:

[1 mark] To deflect ions based on their mass-to-charge ratio ($m/z$). Lighter ions are deflected more than heavier ions.

Question 4: Determine the number of protons, neutrons, and electrons in $^{37}Cl^-$. [2 marks]

Mark Scheme:

[1 mark] Protons = 17, Neutrons = 20 ($37 - 17$)
[1 mark] Electrons = 18 ($17 + 1$ for the negative charge)

Question 5: Explain why isotopes of the same element have the same chemical properties. [1 mark]

Mark Scheme:

[1 mark] They have the same number of electrons / same electron configuration, so they react in the same way.

Question 6: Define the term "relative atomic mass". [2 marks]

Mark Scheme:

[1 mark] The weighted mean/average of the masses of all naturally occurring isotopes of an element.
[1 mark] Relative to $\frac{1}{12}$ the mass of a carbon-12 atom.

Question 7: Outline how Rutherford's gold foil experiment provided evidence for the nuclear model of the atom. [3 marks]

Mark Scheme:

[1 mark] Most alpha particles passed straight through → most of the atom is empty space.
[1 mark] A few were deflected at large angles → the nucleus is positively charged (repels positive alpha particles).
[1 mark] Very few bounced back → the nucleus is very small and dense (concentrated positive charge).

Question 8: Silicon has three isotopes: $^{28}Si$ (92.2%), $^{29}Si$ (4.7%), $^{30}Si$ (3.1%). Calculate the relative atomic mass of silicon. [2 marks]

Mark Scheme:

[1 mark] $A_r = \frac{(28 \times 92.2) + (29 \times 4.7) + (30 \times 3.1)}{100}$
[1 mark] $= \frac{2581.6 + 136.3 + 93.0}{100} = \frac{2810.9}{100} = 28.1$