The density of mobile electrons in copper metal is 84 times

The density of mobile electrons in copper metal is 8.4 times 10^28 m^-3. Suppose that i=8.4 times 10^-18 electrons per second are drifting through the copper wire (a typical value for a simple circuit). 1 he diameter of the wire is 2.6mm. In this case, about how many minutes would it take for a single electron in the electron sea to drift from one end to the other end of a wire that is 23cm long? - 0.3 minutes 25 minutes 97 minutes 204 minutes

Solution

According to the given problem,

As provided in th question, density d = 8.4*10²⁸m^-3, i = 8.4*10¹⁸ electrons/s
diameter D = 2.6 mm = 2.6*10^-3 m
length L = 23 cm = 0.23 m

Now calculate the volume of wire,

V = *(D/2)² *L = *(2.6*10^-3/2)²*0.23

V = 1.22*10^-6 m³

Then the number of electrons to drift is

V*d = 1.22*10^-6 *8.4*10²⁸ = 1.0257*10²³

Every second number of electrons to drift is i = 8.4*10¹⁸ electrons/s

Finally the time is,

t = 1.0257*10²³/ 8.4*10¹⁸ s

t = 12211.370 sec

t = 204 min [4]