3.2.1.1 - Constituents of the Atom

The Structure of the Atom

An atom has a tiny, dense nucleus containing protons and usually neutrons. The common hydrogen-1 nucleus is a single proton. Because protons and neutrons both live in the nucleus, they are collectively called nucleons. Surrounding the nucleus are electrons, which are held in the atom by the electrostatic attraction between their negative charge and the positive charge of the nucleus.

Rutherford's alpha-scattering experiment showed that the nucleus contains almost all of the mass of the atom, even though the atom itself is mostly empty space. The diameter of the nucleus is of order $10^{-15}$ m, compared with about $10^{-10}$ m for the atom as a whole. These sizes differ by about five orders of magnitude. A drawing cannot show both at true scale: the nucleus below is deliberately enlarged, and the circular shell is a simple model, not a measured electron path.

[DIAGRAM: asset_name: 2.1.1 - Constituents of the Atom - Diagram 1; asset_slug: 2.1.1 - Constituents of the Atom - Diagram 1; recommended_method: imagegen; caption: Neutral helium-4: two protons, two neutrons and two electrons. The nucleus is enlarged.; description: Neutral helium-4 has two protons, two neutrons and two electrons; the nucleus is enlarged and the model is not to scale.]

An uncharged atom has equal numbers of protons and electrons, so its total charge is zero. If the atom gains or loses electrons, it becomes an ion.

Charge and Mass of Subatomic Particles

The three subatomic particles differ in both charge and mass. You must know their values in SI units and in relative units, where the magnitude of the proton charge and the proton mass set the reference values.

Three observations matter immediately. The proton and neutron have almost the same mass, the electron is much lighter than either nucleon, and the proton and electron carry charges of equal magnitude but opposite sign.

Because the electron mass is so small compared with the nucleon mass, the mass of an atom is concentrated almost entirely in the nucleus. This is why, when calculating the mass of a nucleus or an ion, the electron mass is usually neglected.

The atomic mass unit (amu) belongs to the later nuclear-physics section, so for this lesson you only need kilograms, relative masses, proton number, nucleon number, and specific charge.

Proton Number, Nucleon Number, and Nuclide Notation

Every element is defined by the number of protons in its nucleus. This is the proton number or atomic number, symbol $Z$.

The total number of protons and neutrons in the nucleus is the nucleon number, symbol $A$.

If you know both $A$ and $Z$, you can find the number of neutrons by subtraction.

We represent a nuclide, meaning a specific nuclear species, using nuclide notation:

Here $X$ is the chemical symbol of the element, $A$ is the nucleon number, and $Z$ is the proton number. For example, ${}^{238}_{92}\text{U}$ has 92 protons and $238 - 92 = 146$ neutrons. In the figure, notice where $A$ and $Z$ sit around the symbol and how the neutron number is found by subtracting $Z$ from $A$.

[DIAGRAM: asset_name: 2.1.1 - Constituents of the Atom - Diagram 2; asset_slug: 2.1.1 - Constituents of the Atom - Diagram 2; recommended_method: retained_png; caption: Carbon-12 has A = 12, Z = 6 and six neutrons.; description: Nuclide notation for carbon-12 showing ${}^{12}_{6}\text{C}$, with labels pointing to $A$ as the nucleon number, $Z$ as the proton number, and a note that the neutron number is $A - Z = 6$.]

Specific Charge

The specific charge of a particle is its charge divided by its mass. It tells you how much charge the particle carries for each kilogram of mass.

This ratio is written using the symbol for charge divided by the symbol for mass.

Here $Q$ is the charge in coulombs, $m$ is the mass in kilograms, and the unit of specific charge is C kg$^{-1}$. Because charge can be positive or negative, specific charge can also be positive or negative.

For a proton,

For an electron,

The electron's specific charge has a much larger magnitude than the proton's because the charges have the same magnitude but the electron has a far smaller mass. In questions, read the sign carefully: electrons have negative specific charge, while positively charged nuclei and positive ions have positive specific charge.

A neutral object has zero specific charge even though it contains charged particles: use its net charge. A negative specific charge does not mean a negative mass.

Isotopes and Isotopic Data

Atoms of the same element always have the same proton number, but they can have different numbers of neutrons. Atoms of the same element with different numbers of neutrons are called isotopes.

For example, carbon has several isotopes:

These are all carbon because they all have proton number 6. They have the same chemical properties because neutral atoms of each isotope have the same number of electrons and therefore the same electron arrangement. Their masses differ because their neutron numbers differ.

Another important use of isotopic data is calculating the mean relative atomic mass of an element from the abundances of its isotopes.

At this stage, the isotope masses are often approximated using their nucleon numbers. For chlorine:

So the mean relative atomic mass is about 35.5 as a dimensionless relative mass.

Calculating Specific Charge of Nuclei and Ions

A nucleus and an ion with the same nucleon number have almost the same mass but very different net charges. A nucleus has no electrons, so its charge is exactly $Ze$. An ion with charge $+ke$ has $Z-k$ electrons: use $ke$, not $Ze$.

Choose the charge before dividing

For a calcium-40 nucleus, $Q=20e=3.20\times10^{-18}\,\mathrm C$ and $m\approx40(1.67\times10^{-27})=6.68\times10^{-26}\,\mathrm{kg}$. Thus $Q/m=4.79\times10^7\,\mathrm{C\,kg^{-1}}$. For a calcium-40 ion with charge $+2e$, the same approximate mass gives $Q/m=4.79\times10^6\,\mathrm{C\,kg^{-1}}$, one tenth as large.

The mass estimate ignores electron mass, the small proton–neutron mass difference and nuclear binding-energy mass differences. It is appropriate for these approximate calculations, not an exact nuclear mass.

For a nucleus, the charge is $Ze$ and the mass is approximately $A \times 1.67 \times 10^{-27}$ kg. For an ion, use the net ionic charge instead of $Ze$, but still treat the mass as approximately $A \times 1.67 \times 10^{-27}$ kg.

This is why isotope separation and isotope detection depend on both charge and mass, not just on the name of the element.

Read questions carefully: a nucleus and an ion of the same element do not have the same total charge, so they do not have the same specific charge.