Chemistry

1.2 - Isotopes & Relative Atomic Mass

9 min

Atomic number & symbols

Relative atomic mass

Calculating Ar

note 1 of 3

What an isotope is

Every atom of an element has the same number of protons in its nucleus.
That proton count is the atomic number (or proton number), and it's what determines which element an atom is.
Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons.

Isotopes have different mass numbers

Mass number (or nucleon number) = number of protons + number of neutrons.
Isotopes of an element share an atomic number but have different mass numbers.
Most elements exist naturally as a mixture of two or more isotopes.

Carbon as an example

Carbon-12 - 6 protons, 6 neutrons, 6 electrons.
Carbon-13 - 6 protons, 7 neutrons, 6 electrons.
Both are carbon because both have 6 protons; they differ only in their neutron count and mass number.

Carbon-12 and carbon-13 atoms side by side, each with 6 electrons in two shells, labelled mass number 12 with 6 protons and 6 neutrons, and mass number 13 with 6 protons and 7 neutrons.

note 2 of 3

Relative atomic mass

Most elements are a mixture of isotopes with different masses, so relative atomic mass ( $A_{r}$ ) is used to describe the element as a whole.
$A_{r}$ is a weighted average of the masses of the different isotopes, taking into account both the mass of each isotope and its relative abundance (how common it is).

Whole number or not

One isotope - $A_{r}$ equals that isotope's mass number, so it's a whole number.
More than one isotope - The average is pulled towards the more common isotope, so $A_{r}$ usually isn't a whole number.
Chlorine is the standard example: it has two main isotopes, chlorine-35 and chlorine-37. Because chlorine-35 is much more abundant, chlorine's $A_{r}$ is 35.5.

A chlorine sample of 100 circles, 25 chlorine-37 (about 25% abundance) and 75 chlorine-35 (about 75% abundance), points to relative atomic mass = 35.5 on a mass number scale from 35 to 37.

Relative atomic mass vs mass number

Mass number - The number of protons plus neutrons in one specific atom (always a whole number).
Relative atomic mass ( $A_{r}$ ) - the average mass of all the isotopes of an element, taking abundance into account (often not a whole number).

Formula for relative atomic mass

$A_{r} = \frac{sum of (abundance \times mass number)}{sum of abundances}$

Where:

$A_{r}$ = Relative atomic mass
Abundance is how common each isotope is, given as a percentage, a fraction, or a ratio of relative amounts
Mass number is the mass number of each isotope

The denominator is the total of the abundances (which equals 100 when abundances are percentages).

note 3 of 3

Worked example - Relative atomic mass of copper

Copper has two stable isotopes. Copper-63 has an abundance of 69.2% and copper-65 has an abundance of 30.8%. Calculate the relative atomic mass of copper to one decimal place.

Step 1 - Multiply each isotope's mass number by its abundance

63 × 69.2 = 4,359.6

65 × 30.8 = 2,002

Step 2 - Add the products together

4,359.6 + 2,002 = 6,361.6

Step 3 - Add the abundances and divide

The abundances are percentages of the same element, so they total 69.2 + 30.8 = 100.

$A_{r} = \frac{6,361.6}{100} = 63.616$

Step 4 - Round to the accuracy asked for

To one decimal place, the relative atomic mass of copper is 63.6.

Step 5 - Interpretation

The answer lies between 63 and 65 and sits nearer to 63, which matches copper-63 being the more abundant isotope.

key terms

TermDefinition

Atomic numberThe number of protons in the nucleus of an atom.

IsotopeOne of two or more forms of the same element whose atoms have the same number of protons but different numbers of neutrons.

Mass numberThe total number of protons and neutrons in the nucleus of an atom.

Relative atomic massThe average mass of an atom of an element, taking into account the abundance (how common) of each isotope. It is measured on a scale where a carbon-12 atom has a mass of exactly 12.

end of notes

Key points to remember

What an isotope is

Every atom of an element has the same number of protons in its nucleus.

That proton count is the atomic number (or proton number), and it's what determines which element an atom is.

Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons.

Isotopes have different mass numbers

Mass number (or nucleon number) = number of protons + number of neutrons.

Isotopes of an element share an atomic number but have different mass numbers.

Most elements exist naturally as a mixture of two or more isotopes.

Carbon as an example

Carbon-12 - 6 protons, 6 neutrons, 6 electrons.

Carbon-13 - 6 protons, 7 neutrons, 6 electrons.

Both are carbon because both have 6 protons; they differ only in their neutron count and mass number.

Relative atomic mass

Most elements are a mixture of isotopes with different masses, so relative atomic mass (

A_{r}

) is used to describe the element as a whole.

A_{r}

is a weighted average of the masses of the different isotopes, taking into account both the mass of each isotope and its relative abundance (how common it is).

Whole number or not

One isotope -

A_{r}

equals that isotope's mass number, so it's a whole number.

More than one isotope - The average is pulled towards the more common isotope, so

A_{r}

usually isn't a whole number.

Chlorine is the standard example: it has two main isotopes, chlorine-35 and chlorine-37. Because chlorine-35 is much more abundant, chlorine's

A_{r}

is 35.5.

Worked example - Relative atomic mass of copper

Copper has two stable isotopes. Copper-63 has an abundance of 69.2% and copper-65 has an abundance of 30.8%. Calculate the relative atomic mass of copper to one decimal place.

Step 1 - Multiply each isotope's mass number by its abundance

63 × 69.2 = 4,359.6

65 × 30.8 = 2,002

Step 2 - Add the products together

4,359.6 + 2,002 = 6,361.6

Step 3 - Add the abundances and divide

The abundances are percentages of the same element, so they total 69.2 + 30.8 = 100.

$A_{r} = \frac{6,361.6}{100} = 63.616$

Step 4 - Round to the accuracy asked for

To one decimal place, the relative atomic mass of copper is 63.6.

Step 5 - Interpretation

The answer lies between 63 and 65 and sits nearer to 63, which matches copper-63 being the more abundant isotope.