If an ion has 14 electrons but a relative charge of plus two, how many protons are in the nucleus of the ion?
As we get started with this question, we recognize that an ion is an atom that has an overall or net charge to it. This particular ion has an overall charge of plus two, meaning that however many electrons it has, which each represent a single negative charge, it has two more protons. We could draw this ion, which is an atom, this way. Here is the nucleus, the centre of the atom. This is where all the protons and the neutrons in the atom reside. And then, outside the nucleus and orbiting around it are the electrons of the ion.
We’re told that there are one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14 electrons. But if we consider the ion overall, it has a net positive charge of plus two. Since each individual electron has a net charge of negative one, that means the total charge from all 14 electrons is negative one times 14 or negative 14. But since we knew that the overall charge of this ion is plus two, we basically end up with an equation. This equation says that the overall charge of the electrons, negative 14, plus the overall charge of the protons, we’ll call it 𝐶 sub p, is equal to positive two.
At this point, it’s important to realise that each individual proton has an overall charge represented by positive one. This means that the total charge of the protons, what we’re calling 𝐶 sub p, is also equal to the total number of protons. So now that we have this equation, we can solve it for 𝐶 sub p, the total charge of the protons in this nucleus. If we add positive 14 to both sides of the equation, then that 14 cancels out with the negative 14 on the left-hand side. And on the right-hand side, we have positive two plus 14. That equals 16. The total charge, therefore, of the protons in this ion is positive 16.
And as we said, since each proton represents one positive charge, that means that this is also equal to the number of protons in the nucleus of this ion. That number then is 16.