Calculating Protons Neutrons and Electrons
Standard notation for atoms and ions encodes their fundamental composition, so you can 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.