Revise Isotopes for Cambridge 9701 (1.2)

All atoms of a specific element must have the same number of protons; this is their atomic number ($Z$). However, they can have different numbers of neutrons. Atoms that share the same atomic number but have different numbers of neutrons are called isotopes. Since the mass number ($A$) is the sum of protons and neutrons, isotopes of an element will have different mass numbers.

The mass of an element you see on the periodic table is not the mass of a single atom. Instead, it is the relative atomic mass ($A_r$), which is a weighted average of the masses of its naturally occurring isotopes. This average takes into account the relative abundance of each isotope – the more common an isotope is, the more it influences the final $A_r$. The standard for comparison is the carbon-12 isotope, which is assigned a mass of exactly 12.

$A_r = \frac{\sum(\text{isotopic mass} \times \text{\% abundance})}{100}$

Since isotopes of an element have the identical electron configuration (the same number of electrons in the same orbitals), they exhibit the same chemical properties. They react in exactly the same way. However, their physical properties, which depend on mass, can differ slightly. Heavier isotopes diffuse more slowly and have slightly higher densities and boiling points. The most significant difference arises when an isotope is unstable. These 'radioisotopes' have an unstable neutron-to-proton ratio in their nucleus, causing them to undergo radioactive decay. This property is harnessed in applications like carbon-14 dating, medical imaging (e.g., PET scans using fluorine-18), and cancer therapy (e.g., cobalt-60).