Question

How does the number of electrons relate to an element's atomic number? Why?

Answer 1

The number of protons in the nucleus of the atom is equal to the atomic number. The number of electrons in a neutral atom is equal to the number of protons. The mass number of the atom is equal to the sum of the number of protons and neutrons in the nucleus.
Hope it helped

Answer 2

The number of electrons equals the number of protons in a neutral atom (ie something that isn't an ion), and in turn the number of protons determine the atomic number (and therefore its chemical identity).

If we're talking about ions then the number of electrons does not match up with the atomic number. For example, the potassium ion $K^{+}$ has 18 electrons. It lost an electron which gives it a charge of +1, yet it's proton count is 19 and so is the atomic number.