Particle numbers, isotopes and relative atomic mass

Two numbers that describe an atom

An atom has protons and neutrons in its nucleus, with electrons outside the nucleus. Counting these particles tells us which element the atom belongs to and which isotope it is.

The atomic number, $Z$, is the number of protons in the nucleus. Every atom of a particular element has the same number of protons, and this number is unique to that element. For example, every lithium atom has three protons, whereas every beryllium atom has four. Changing the number of protons means changing the element.

The mass number, $A$, is the total number of protons and neutrons in one atom’s nucleus:

$$A = \text{number of protons} + \text{number of neutrons}$$

Mass number is a particle count, so it is always a whole number. It does not include electrons.

Reading symbols and finding particle numbers

An atom can be represented as ${}^{A}_{Z}\mathrm{X}$, where X is the chemical symbol. The mass number is written at the upper left and the atomic number at the lower left.

For example, ${}^{14}_{6}\mathrm{C}$ represents carbon with atomic number 6 and mass number 14. It can also be called carbon-14 or written C-14. The 14 is the total number of protons and neutrons, not the number of neutrons alone.

To find the particles in a neutral atom:

• Protons: equal to the atomic number, $Z$.
• Neutrons: mass number minus atomic number, $A-Z$.
• Electrons: equal to the number of protons, because an atom has no overall charge.

For carbon-14, there are 6 protons and $14-6=8$ neutrons. Its 6 electrons balance the positive charge of its 6 protons.

As another example, an atom with atomic number 29 and mass number 63 has 29 protons, 29 electrons and $63-29=34$ neutrons. Together, the 29 protons and 34 neutrons account for its mass number of 63.

Isotopes: the same element, different neutron numbers

Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons in their nuclei. Their atomic numbers are identical, but their mass numbers differ.

Compare these two carbon atoms:

Both are carbon because both have six protons. Carbon-14 has one more neutron, giving it a greater mass. Isotopes have the same chemical properties because their neutral atoms have the same electron arrangement, including the same number of outer-shell electrons.

Why relative atomic mass can be a decimal

A sample of an element may contain a mixture of isotopes. The relative atomic mass, $A_\mathrm{r}$, describes their average relative mass, taking account of how common each isotope is. It is therefore a : an abundant isotope contributes more to the average than a rare isotope.

This explains why some relative atomic masses are not whole numbers. The average can lie between the masses of the isotopes present. It does not mean that an individual atom contains a fraction of a proton or neutron.

Mass number and relative atomic mass describe different things. Mass number counts particles in one atom’s nucleus; relative atomic mass averages the relative masses of atoms in a sample. For example, lithium’s relative atomic mass is about 6.94, although a GCSE periodic table may show it rounded to 7.

Calculating a weighted mean — Higher tier

Multiply each isotope’s relative mass by its abundance, add these contributions, then divide by the total abundance:

$$A_\mathrm{r}=\frac{\text{sum of (isotope relative mass × abundance)}}{\text{total abundance}}$$

For percentage abundances, the denominator is 100. For abundances given as a ratio or relative numbers, use their total instead. Include a contribution from every isotope listed.

Consider a rubidium sample containing 72% rubidium-85 and 28% rubidium-87, using relative isotope masses of 85 and 87:

$$A_\mathrm{r}=\frac{(85\times72)+(87\times28)}{100}=85.56$$

To one decimal place, the relative atomic mass of this sample is 85.6. It has no unit. The result lies between 85 and 87 and is closer to 85 because rubidium-85 is more abundant. Simply averaging 85 and 87 would give 86, but that would incorrectly treat the two isotopes as equally abundant.

Particle numbers

For ${}^{A}_{Z}\mathrm{X}$:

• Protons $=Z$.
• Neutrons $=A-Z$.