And we don't even have to know that the element is gold. If #Z# #=# #79#, there are 79 positively charged nuclear particles, 79 protons, in the nucleus. If 79 nuclear charges, the NEUTRAL atom contains 79 electrons. You specified an ion, and gold forms both #Au^+# and #Au^(3+)# ions so #78# and #76# electrons respectively.
Now, it is a fact that the atomic mass of gold is #196.97# #g*mol^-1#, roughly close to #197#. Because the atomic mass is #197# #"amu"#, there must be #197-79= 118 " neutrons"#, massive, neutrally charged "nucular" particles. Atomic mass is to a first (and second) approximation, the sum of the protons and neutrons (there will be a mixture of isotopes because of different numbers of neutrons), because electrons have negligible mass.
Now if #Z# #=# #78#, can you tell me the element, the number of protons, the number of neutrons, and the number of electrons?
