Atomic structure

Every atom is made of three subatomic particles. The protons and neutrons sit together in a tiny central nucleus; the electrons occupy the much larger volume around it.

| Particle | Relative charge | Relative mass |

|---|---|---|

| Proton | $+1$ | $1$ |

| Neutron | $0$ | $1$ |

| Electron | $-1$ | $\approx \frac{1}{1836}$ (negligible) |

Key ideas:

• The nucleus is positively charged (protons) and holds almost all the mass, yet it is extremely small compared with the whole atom - most of an atom is empty space.
• In a neutral atom, protons = electrons, so the charges cancel.
• The atomic (proton) number $Z$ is the number of protons; it defines the element.
• The mass number $A$ counts the nucleons (protons + neutrons), so $\text{neutrons} = A - Z$.

Nuclide symbol notation places $A$ on top and $Z$ on the bottom, e.g. $^{23}_{11}\text{Na}$ has $11$ protons, $11$ electrons and $23 - 11 = 12$ neutrons.

Ions form by transferring electrons: gaining electrons makes a negative anion (e.g. $\text{Cl}^-$ has one extra electron), losing electrons makes a positive cation (e.g. $\text{Na}^+$ has one fewer). The proton number never changes when an ion forms - only the electron count does.

Isotopes are atoms of the same element (same $Z$, same number of protons and electrons) but with different numbers of neutrons, so they have different mass numbers $A$.

For example, chlorine exists as $^{35}_{17}\text{Cl}$ and $^{37}_{17}\text{Cl}$: both have $17$ protons, but $18$ and $20$ neutrons respectively.

Consequences:

• Chemical properties are identical, because chemistry depends on the electron arrangement, which is the same for all isotopes of an element.
• Physical properties differ slightly, because they depend on mass - heavier isotopes have greater density and diffuse/effuse more slowly.

Because a real sample is a mixture of isotopes, we use a weighted average mass called the relative atomic mass $A_r$:

$$A_r = \frac{\sum(\text{isotopic mass} \times \text{abundance})}{\sum \text{abundance}}$$

$A_r$ is measured on the scale where one carbon-12 atom is defined as exactly $12$, so it is a ratio with no units. This is why periodic-table values like $\text{Cl} = 35.45$ are not whole numbers - they reflect the mix of isotopes, weighted by abundance, not the mass of any single atom.

A mass spectrometer measures the masses and abundances of the particles in a sample, allowing the relative atomic mass of an element to be found experimentally. The main stages are:

• Ionisation - atoms or molecules are converted to positive ions (commonly by knocking off electrons).
• Acceleration - the ions are accelerated by an electric field.
• Deflection/separation - ions are separated according to their mass-to-charge ratio ($m/z$); lighter ions (smaller $m/z$) are deflected more.
• Detection - the detector records the relative abundance of ions at each $m/z$ value.

The result is a mass spectrum: a graph of relative abundance against $m/z$. For singly charged ions ($z = 1$), the $m/z$ value equals the relative mass of the ion, so each isotope gives a separate peak.

To find $A_r$, take the $m/z$ values as the isotopic masses and combine them with the abundances:

$$A_r = \sum\left(\text{isotopic mass} \times \frac{\% \text{abundance}}{100}\right)$$

Mass spectrometry both proves the existence of isotopes (multiple peaks for one element) and gives the data needed to calculate $A_r$. A characteristic example is bromine, whose two isotopes of near-equal abundance give an $A_r$ close to $80$.