Structure 1.2.2 – Isotopes and Relative Atomic Mass

Isotopes

Isotopes are atoms of the same element that have:

• • The same number of protons (and electrons, if neutral)
  • Different number of neutrons

This means their atomic number \( Z \) is the same, but their mass number \( A \) is different.

• Since the electron arrangement remains unchanged, all isotopes of an element have identical chemical properties.
• However, due to the difference in mass, they may show differences in physical properties.

Physical Property Differences Between Isotopes:

• Mass: Heavier isotopes have greater mass.
• Density: Heavier isotopes tend to be more dense.
• Boiling and melting points: These may be slightly higher for heavier isotopes.
• Rate of diffusion: Lighter isotopes diffuse faster (Graham’s law of diffusion).
• Vibrational energy (IR): Used in spectroscopy to distinguish isotopes.

 Representation of Isotopes:

Isotopes are written using nuclear notation:

\( {}^A_Z\text{X} \),

where:

• \( A \) = mass number = number of protons + neutrons
• \( Z \) = atomic number = number of protons
• \( \text{X} \) = chemical symbol of the element

Example: Isotopes of hydrogen:

• \( {}^1_1\text{H} \) – 1 proton, 0 neutrons (hydrogen-1)
• \( {}^2_1\text{H} \) – 1 proton, 1 neutron (deuterium)
• \( {}^3_1\text{H} \) – 1 proton, 2 neutrons (tritium)

Relative Atomic Mass (A_r):

The relative atomic mass is the weighted average mass of all isotopes of an element based on their natural abundance.

Formula:

\( A_r = \frac{(a_1 \times m_1) + (a_2 \times m_2) + \ldots}{100} \)

• \( a_1, a_2, \ldots \) are the percentage abundances
• \( m_1, m_2, \ldots \) are the relative masses of each isotope

Note: The resulting \( A_r \) value is usually a non-integer.