(a) Estimate the average drift speed of conduction electrons in a copper wire of cross- sectional area 1.0x10-7 m carrying a current of 1.5A. Assume that each copper atom contributes roughly one conduction electron. The density of copper is 9.0x10kg/m, and its atomic mass is 63.5 u.

Sol84:

To estimate the average drift speed of conduction electrons, we can use the formula:

I = nAqv

where:

• I is the current (1.5 A)
• n is the number of conduction electrons per unit volume (equal to the number of copper atoms per unit volume, since each copper atom contributes roughly one conduction electron)
• A is the cross-sectional area (1.0x10^-7 m^2)
• q is the charge of an electron (-1.6x10^-19 C)
• v is the average drift speed we want to find

First, we need to find n. The density of copper is given as 9.0x10^3 kg/m^3, and its atomic mass is 63.5 u. One mole of copper has a mass of 63.5 g, which contains Avogadro\\\'s number (6.02x10^23) of atoms. So the volume occupied by one mole of copper is:

V = m / (?N) where:

• m is the mass of one mole of copper (63.5 g)
• ? is the density of copper (9.0x10^3 kg/m^3)
• N is Avogadro\\\'s number (6.02x10^23)

Plugging in the numbers, we get:

V = (63.5 g) / (9.0x10^3 kg/m^3 x 6.02x10^23) = 7.11x10^-6 m^3/mol

Since one mole of copper contains Avogadro\\\'s number of atoms, the number of copper atoms per unit volume is:

n = N/V = (6.02x10^23) / (7.11x10^-6 m^3/mol) = 8.46x10^28 m^-3

Now we can solve for v:

v = I / (nAq)

Plugging in the numbers, we get:

v = (1.5 A) / (8.46x10^28 m^-3 x 1.0x10^-7 m^2 x -1.6x10^-19 C) = -1.11x10^-4 m/s

Note that the negative sign just indicates that the electrons are moving in the opposite direction to the conventional current. The magnitude of the drift speed is approximately 0.1 mm/s, which is very small compared to the speed of individual electrons in the wire (on the order of millions of meters per second).