Question

An electrically neutral coin of mass 3g is made up of pure copper. Find the magnitude of total charge on the coin?

Answer 1

A neutral atom has a negative charge of magnitude Ze associated with its electrons and a positive charge of the same magnitude associated with the protons in its nucleus, where Z is the atomic number of the element in question. For copper, Z = 29, which means that an atom of copper has 29 protons and, when neutral, 29 electrons.
The charge magnitude q we seek is equal to NZe, in which N is the number of atoms in the penny. To find N, we multiply the number of moles of copper in penny by the number of atoms in a mole (Avogadro’s number, $N_A=6.02\times {10}^{23}$ atoms/mol). The number of moles of copper is 63.5 g/mol. Thus we have
$N=N_A\left(m/M\right)=(6.02\times {10}^{23}$ atoms/mol) (3 g/63.5 g/mol)
$=2.85\times {10}^{22}atoms$
We then find the magnitude of the total positive or negative charge in the penny to be,
q = NZe
$=(2.85\times {10}^{22})\left(29\right)(1.60\times {10}^{-19}C)$
=132240C