a How many conduction electrons are there in a 10mmdiameter

(a) How many conduction electrons are there in a 1.0-mm-diameter gold wire that is 9 cm long?

(b) How far must the sea of electrons in the wire move to deliver -32 nC of charge to an electrode? In meters

Solution

(a)  volume = (pi) x R^(2) x L, where pi = 3.1416, R = 1 mm = 0.1 cm, and L = 9 cm.

V = 2.826x 10^(-2) cm^3.
No. of free electrons per cm^3 = 5.90 x 10^(22)
Total no. of free (conduction) electrons=2.826x 10^(-2) x 5.9 x 10^(22) = 1.67 x 10^(21)

(b) No. of electrons = -32 x 10^(-9)/1.6 x 10^(-19)  = 2 x 10^(11)

Volume of 2 x 10^(11) electrons = 2 x 10^(11) / 5.90 x 10^(22) = 3.4 x 10^(-12) cm³

Length of wire = 3.4 x 10^(-12) x 4 / 3.14 x 0.01 = 4.3 x 10^-10 cm = 4.3 * 10^(-12) m