Consider a copper wire with a diameter of 2.43 mm. (a) What is the drift speed o

Question

Consider a copper wire with a diameter of 2.43 mm. (a) What is the drift speed of the electrons in the copper wire when a current of 11.0 A flows through it? Assume that each copper atom contributes one free electron to the metal. The density of copper is 8.92 g/cm3 How is the drift speed related to the current flowing in a wire? Consider the fact that there is one free electron per copper atom when determining the charge density (b) How does this drift speed compare to the random rms speed of an electron at 20.0°C? To make this comparison, determine the random rms speed of an electron at 20.0°C using the ideal gas model and find the ratio of the two speeds. Vrms = Vd Review the iuearyd Enter a number del. How is the rms speed related to the temperature and mass?

Explanation / Answer

Given,

d = 2.43 mm

a)I = 11 A ; rho = 8.92 g/cm^3 = 8920 kg/m^3

m(1 mol) = 63.5 g

N = 8920/63.5 x 10^-3 = 1.4 x 10^5 moles

No of free electrons will be:

N = 1.4 x 10^5 x 6.023 x 10^23 = 8.43 x 10^28 electrons

We know that

I = n e A vd

vd = I/(n e A)

vd = 11/(8.43 x 10^28 x 1.6 x 10^-19 x 3.14 x (1.215 x 10^-3)^2) = 1.76 x 10-4 m/s

Hence, vd = 1.76 x 10^-4 m/s

b)Vrms = sqrt (3RT/M)

Vrms = sqrt (3 x 8.4 x 293/5.84 x 10^-7) = 1.12 x 10^5 m/s

R = 1.12 x 10^5/1.76 x 10^-4 = 6.36 x 10^8

Hence, R = 6.36 x 10^8

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