S1.2.2 Isotopes

Isotopes and Their Properties

You're comparing coins of the same currency.
Some are slightly heavier than others because they contain more metal, yet they belong to the same denomination and have the same face value.

This is similar to how isotopes work in chemistry.

What Are Isotopes?

Atoms are defined by their number of protons, known as the atomic number (Z).
However, atoms of the same element can have different numbers of neutrons, which changes their mass number (A).

These different versions of the same element are called isotopes.

Definition of Isotopes

Definition

Isotopes

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

This means isotopes share:

The same atomic number (Z), since the number of protons determines the element.
Different mass numbers (A), because the mass number is the sum of protons and neutrons.

Example

Chlorine isotopes

Chlorine-35 ( $^{35} Cl$ ) has 17 protons and 18 neutrons.
Chlorine-37 ( $^{37} Cl$ ) has 17 protons and 20 neutrons.

Note

The chemical properties of isotopes are nearly identical because chemical behavior depends on the number of electrons, which remains the same for all isotopes of an element.

Relative Atomic Mass and Isotopic Abundance

Take a look at the periodic table.
You’ll notice that atomic masses of elements are rarely whole numbers.
For instance, chlorine’s relative atomic mass ( $A_{r}$ ) is 35.45, even though its isotopes have whole-number mass numbers (35 and 37). Why is this?

Definition

Relative atomic mass

The relative atomic mass of an element is a weighted average of the masses of its isotopes, based on their natural abundances, compared to 1/12th the mass of a carbon-12 atom. Since it is a ratio, $A_{r}$ has no units.

Definition

Relative abundance

Relative abundance refers to the percentage of a specific isotope of an element present in a naturally occurring sample.

It indicates how common each isotope is compared to the total amount of the element, which is used to calculate the element's average atomic mass.

Calculating Relative Atomic Mass

To calculate the relative atomic mass ( $A_{r}$ ), use the formula:

$A_{r} = \frac{(mass of isotope 1 × % abundance of isotope 1) + (mass of isotope 2 × % abundance of isotope 2) + \dots}{100}$

Example

Relative atomic mass of chlorine

Chlorine has two isotopes:

Chlorine-35 ( $^{35} Cl$ ) with 75.8% abundance.
Chlorine-37 ( $^{37} Cl$ ) with 24.2% abundance.

Calculate the relative atomic mass:
$A_{r} = \frac{(35 \times 75.8) + (37 \times 24.2)}{100}$

Step-by-step:

Multiply each isotope’s mass by its abundance:
$35 \times 75.8 = 2653$ and $37 \times 24.2 = 895.4$
Add these values together:
$2653 + 895.4 = 3548.4$
Divide by 100 to find the average:
$A_{r} = \frac{3548.4}{100} = 35.48$

Thus, the relative atomic mass of chlorine is approximately 35.45.

Tip

Before starting your calculation, double-check that the percentage abundances add up to 100% to avoid errors.

Determining Percent Abundances

To determine percent abundance from the relative atomic mass ( $A_{r}$ ) and mass numbers of isotopes, use the weighted average formula:

$A_{r} = (m_{1} \times %_{1} ) + (m_{2} \times %_{2} )$

where $m_{1}$ and $m_{2}$ are the mass numbers of the isotopes, and $%_{1} + %_{2} = 1$ . If the percent abundance of one isotope is unknown, let $%_{1} = x$ and solve using:

$A_{r} = (m_{1} \times x) + (m_{2} \times (1 - x))$

Rearrange the equation to solve for $x$ , then multiply by 100 to express the abundance as a percentage.

Note

This method can be extended for elements with more than two isotopes.

Physical Properties of Isotopes

While isotopes of the same element have nearly identical chemical properties, their physical properties can differ.
These differences arise because isotopes have different masses, which can impact properties like density, melting point, and boiling point.

Example

Hydrogen Isotopes:

Protium ( $^{1} H$ ): The most common isotope, with 1 proton and no neutrons.
Deuterium ( $^{2} H$ ): A heavier isotope, with 1 proton and 1 neutron.
Tritium ( $^{3} H$ ): A radioactive isotope, with 1 proton and 2 neutrons.

Example

Uranium Isotopes:

Uranium-235 ( $^{235} U$ ): Used in nuclear reactors and weapons.
Uranium-238 ( $^{238} U$ ): More abundant but less useful for nuclear reactions.

The slight difference in mass allows these isotopes to be separated using methods like gas centrifugation.

Common Mistake

Don’t confuse physical property differences of isotopes with their chemical properties. Isotopes react chemically in the same way because they have the same number of electrons.

Reflection and Self-Review

Self review

What are the key differences between isotopes of the same element?
Why do isotopes have the same chemical properties but different physical properties?
Calculate the relative atomic mass of an element with the following isotopes:
- Isotope A: mass = 10, abundance = 20%
- Isotope B: mass = 11, abundance = 80%.

You've read 2/2 free chapters this week.

Upgrade to PLUS or PRO to unlock all notes, for every subject.

S1.2.2 Isotopes

Isotopes and Their Properties

What Are Isotopes?

Definition of Isotopes

Chlorine isotopes

Relative Atomic Mass and Isotopic Abundance

Calculating Relative Atomic Mass

Relative atomic mass of chlorine

Determining Percent Abundances

Physical Properties of Isotopes

Hydrogen Isotopes:

Uranium Isotopes:

Reflection and Self-Review

You've read 2/2 free chapters this week.

Introduction to Isotopes