Here is a question in physics that I need help with. Can someone please help? Co

Question

Here is a question in physics that I need help with. Can someone please help?

Consider a copper wire with a diameter of 1.91 mm. (a) What is the drift speed of the electrons in the copper wire when a current of 14.0 A flows through it? Assume that each copper atom contributes one free electron to the metal. The density of copper is 8.92 g/cm^3. m/s (b) How does this drift speed compare to the random rms speed of an electron at 20.0 degree C? To make this comparison, determine the random rms speed of an electron at 20.0 degree C using the ideal gas model and find the ratio of the two speeds. Vrms/Vd = _____________________

Explanation / Answer

Part A)

The molar mass of copper is 63.5 g/mol and the density is 8.92 g/cm3

Thus the volume of copper, from the density formula, is

V = m/p = 63.5/8.92 = 7.1188 cm3

Now we can find the number of free electrons per cm3

n = (6.02 X 1023)/(7.1188)

n = 8.46 X 1022 electrons per cm3

That is 8.46 X 1028 m3

Then vd = I/nqA

vd = (14)/(8.46 X 1028)(1.6 X 10-19)(pi)(9.55 X 10-4)2

vd = 3.61 X 10-4 m/s

Part B)

vrms = sqrt(3kbT/m)

vrms = sqrt(3)(1.38 X 10-23)(293)/(9.11 X 10-31)

vrms = 1.15 X 105 m/s

Divide the two...

(1.15 X 105)/(3.61 X 10-4) = 3.20 X 108

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