Every element has a unique identity, a fundamental property that distinguishes it from all others. This identity isn't determined by its size, mass, or the number of electrons it has, but by a single, unchanging number: the count of protons in its nucleus. This is the element's atomic number.

If you change the number of protons, you change the element entirely. An atom with six protons is always carbon. Add one more proton, and it becomes nitrogen. Remove one, and it becomes boron. It's that simple. The atomic number is like an element's fingerprint.

While protons define the element, they don't account for all of the atom's mass. The nucleus also contains neutrons, which have a similar mass to protons. The total count of both protons and neutrons gives us the atom's mass number.

To communicate information about a specific atom quickly, chemists use a standard notation. This format neatly packs the mass number, atomic number, and element symbol together.

Let's look at the most common form of carbon, carbon-12. Its notation is $_{6}^{12}C$. From this, we can figure out everything we need to know about its subatomic particles:

• Protons: The atomic number ($Z$) is 6, so it has 6 protons.
• Electrons: In a neutral atom, the number of electrons equals the number of protons. So, it has 6 electrons.
• Neutrons: The mass number ($A$) is 12. We can find the neutron count by subtracting the atomic number from the mass number: $12 - 6 = 6$ neutrons.

But what happens if we change the number of neutrons? Consider carbon-14, which has the notation $_{6}^{14}C$. It still has 6 protons, so it's still carbon. However, its neutron count is now $14 - 6 = 8$. This makes it an isotope of carbon.

The nucleus is a crowded place. All those positively charged protons are crammed together, and they should be repelling each other with immense force. The atom is held together by two key forces. First, the powerful electrostatic attraction between the positively charged nucleus and the negatively charged electrons orbiting it keeps the electrons bound to the atom.

Second, within the nucleus itself, neutrons play a crucial role as stabilisers. They add mass and contribute to the strong nuclear force—an incredibly powerful but short-range force that overcomes the electrostatic repulsion between protons, effectively gluing the nucleus together. An imbalance in the proton-to-neutron ratio can make a nucleus unstable.

Atoms with a stable combination of protons and neutrons exist in a 'band of stability'. If an isotope has too many or too few neutrons for its number of protons, it falls outside this band. The nucleus becomes unstable and will eventually decay, releasing energy and particles to transform into a more stable configuration. This is the basis of radioactivity. Carbon-14, with its excess neutrons, is a perfect example of such an unstable isotope.

Understanding these relationships between protons, neutrons, and electrons is fundamental. It explains not only why elements are different but also why some versions of an element are stable while others are not.