Question

A current of 50.0A flows through a cross-section of a wire. After six hours, what is the total mass of all of the electrons which have passed through the cross section? Give your answer in milligrams (mg) and to three significant figures.

Answer 1

Given:

$I=50.0\:\rm A$

$t=6\:\rm hr=21600\:\rm s$

$m_e=9.1*10^{-31}\:\rm kg$

$e=1.6*10^{-19}\:\rm C$

The number of electrons passed through the wire cross section

$$N=\frac{q}{e}=\frac{It}{e}\\ =\frac{50.0*21600}{1.6*10^{-19}}=6.75*10^{24}\quad \rm (electrons)$$

The total mass of all electrons which have passed through the cross section

$$m=Nm_e\\ ={6.75*10^{24}*9.1*10^{-31}\:\rm kg}\\ =6.14*10^{-6}\:\rm kg=6.14\:mg$$