Final answer:
To determine the mass of a system with 320 protons and a net charge of -51e, one needs to find the number of electrons to reach that net charge, then calculate and add up the mass of both the protons and electrons in atomic mass units (amu).
Step-by-step explanation:
The student asks about a system with 320 protons and a total charge of -51e and wishes to know the mass of the system. Since each proton and electron has the same magnitude of charge, we can determine the number of electrons necessary to result in a net charge of -51e. Subtracting the charge of the protons, which contribute a charge of +320e, we have:
Total charge = Charge from protons + Charge from electrons
-51e = 320e + Charge from electrons
Charge from electrons = -51e - 320e = -371e
This shows there must be 371 electrons, each with a charge of -1e, to result in a total charge of -51e. To calculate the mass of the system, we must add the mass of protons and the mass of electrons. While the electron mass is negligible compared with the proton mass, for precision, we consider the mass of both subatomic particles. Each electron has a mass of approximately 0.00055 amu, and each proton has a mass of 1.0073 amu.
Total mass of the system = Mass of protons + Mass of electrons
Mass of protons = 320 protons × 1.0073 amu per proton
Mass of electrons = 371 electrons × 0.00055 amu per electron
The next step is to calculate these amounts and sum them up to obtain the mass of the system in amu (atomic mass units).