How do I do this electrical physics problem?

Question

A system has 1525 particles of protons and electrons, and a net charge of -5.456*10^-17.
How many electrons are there and what is the mass of these electrons?
How do I do this?

Answer 1

You have a bit of a problem ;-)

Positive and negative charge will neutralize each other so you do not know how many negative/positive pairs (N/PP) you have.

We can say that
a+b=1525
also if we subtract twice the N/NP from the total we get
1525-2b = ( net charge)/charge of a single electron =Q/e
e= 1.602 E-19 C

Q/e =-5.456*10^-17/1.602 E-19 = 340 electrons (unpaired)
So now we have

a + b = 1525
1525 – 2b=340

b= (1525 – 340)/2=592 protons
a=1525-b
a=1525-592=933 electrons

Total mass of the electrons then is

Mass (e) =933(9.109 E–31 kg)
Mass (e) = 8.498697 E-28 kg

Answer 2

Let x be the number of protons and y be the number of electrons.
The charge on a proton is 1.602*10^(-19)C and the charge on an electron is -1.602*10^(-19)C so
1.602*10^(-19)x - 1.602*10^(-19)y = -5.456*10^(-17)
x + y = 1525
The mass of an electron is 9.108*10(-31) Kg.

HTH ☺

Doug