Calculating Protons Neutrons and Electrons
This topic covers the standard notation for atoms and ions, which encodes their fundamental composition. Mastering this allows you to quickly determine the number of protons, neutrons, and electrons in any species, a core skill for solving many chemistry problems without a calculator.
Part of the ESAT Chemistry syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- An element is defined exclusively by its atomic number (Z), which is the number of protons in its nucleus.
- The mass number (A) represents the total count of particles in the nucleus (protons + neutrons) and approximates the atomic mass.
- In a neutral atom, the number of electrons is equal to the number of protons, resulting in no overall charge.
- Ions are formed when atoms gain or lose electrons, creating a net negative or positive charge respectively. The number of protons in the nucleus remains unchanged during this process.
Formulae
Number of neutrons = A - Z To calculate the number of neutrons in a nucleus when you know the mass number (A) and atomic number (Z).
Number of electrons = Z - (charge) To calculate the number of electrons in an ion. Remember that the charge is positive for cations (e.g., +2) and negative for anions (e.g., -1).
Definitions
- Atomic Number (Z)
- The number of protons in an atom's nucleus. It is the unique identifier for a chemical element.
- Mass Number (A)
- The total number of protons and neutrons in an atom's nucleus.
- Standard Atomic Notation
- A representation of an element written as AZX, where A is the mass number (top), Z is the atomic number (bottom), and X is the element symbol.
Worked example
An ion X²⁺ has 18 electrons and 20 neutrons. What is the mass number of this ion?
- 1
The ion has a charge of +2 and contains 18 electrons.
An ion with a +2 charge has lost 2 electrons.
- 2
To find the number of protons (the atomic number, Z), we reverse the process:
a neutral atom of X would have 18 + 2 = 20 electrons.
Therefore, Z = 20 protons.
- 3
The mass number (A) is the sum of protons and neutrons.
- 4
Calculate A:
A = (number of protons) + (number of neutrons) = 20 + 20 = 40
Answer: 40
Common mistakes
- ×Making sign errors when calculating electrons for ions. A common mistake is to subtract electrons for a negative ion instead of adding them. Remember: a negative charge means an excess of electrons.
- ×Confusing the mass number (A) and atomic number (Z) in standard notation. Always remember A is written Above and Z is written below.
- ×Forgetting that the question might ask for the properties of a neutral atom even when providing data for an ion. The proton and neutron count will be the same, but the electron count will differ.
- ×Simple arithmetic mistakes under pressure, especially when subtracting Z from A to find the number of neutrons.
No-calculator tips
- ✓To find the number of electrons in an ion, tell yourself a story instead of relying purely on a formula. For O²⁻ (Z=8), think 'It's an oxygen atom that has gained two electrons', so it has 8 + 2 = 10 electrons.
- ✓When subtracting to find the neutron count (A - Z), break the subtraction into easier steps. For ⁹⁰₃₈Sr, calculate 90 - 38 as (90 - 30) - 8, which is 60 - 8 = 52.