Calculating relative atomic mass

In a nutshell

Isotopes are atoms of an element with a different number of neutrons. The relative atomic mass can be calculated for isotopes using their abundances.

Isotopes

Definition

Isotopes are atoms of the same element that contain the same number of protons but a different number of neutrons.

Compared to an atom of an element isotopes have:

Same atomic number (the number of protons in an atom)
Different mass number (the number of protons and neutrons in an atom)
Same chemical reactivity (the number of electrons is the same)

Example

The most common isotope of carbon contains $6$ protons and $6$ neutrons, ${12 \atop 6}C$ . ${14 \atop 6}C$ is another less common isotope of carbon. For each isotope, state the mass number, atomic number, number of protons and number of neutrons.

Isotope	Atomic number	Number of protons	Number of neutrons
${12 \atop 6}C$	$12$	$6$	$6$
${14 \atop 6}C$	$14$	$6$	$8$

Relative atomic mass (A $_r$ )

Definition

The relative atomic mass is the average weighted mass of the atoms of an element, compared to $1/12th$ of the mass of a carbon- $12$ atom. The relative atomic mass of an element is calculated using the mass number and abundance of the isotopes. Abundance is when there is a lot of an isotope.

Example

Two isotopes of nitrogen are ${14 \atop 7}N$ and ${15 \atop 7}N$ . The abundance of nitrogen- $14$  is $60$ % and the abundance of nitrogen- $15$  is $40$ %. Work out the relative atomic mass of nitrogen.

Work out the total mass of nitrogen atoms:

$(60\times14) + (40 \times15) = 1440$

Work out the total number of nitrogen atoms:

$(60+40) = 100$

Calculate the relative atomic mass:

$Relative\ atomic\ mass=\frac{Total\ mass\ of\ nitrogen\ atoms}{Total\ number\ of\ nitrogen\ atoms}$

$Relative\ atomic\ mass=\frac{1440}{100}=14.4$

The relative atomic mass of nitrogen is $\underline{14.4}$ .