a. A wire made from aluminum with a cross-section of diameter 0.850 mm carries a

Question

a. A wire made from aluminum with a cross-section of diameter 0.850 mm carries a current of 14.0 A. Calculate the "areal current density"; in other words, how many electrons per square meter per second flow through this wire?

b.The density of aluminum is 2.70 g/cm3, and its atomic mass is 27.4. Assuming each aluminum atom contributes three mobile electrons to the metal, what is the number density of free charges in the wire, in electrons/m3?

c. How many atoms of aluminum are in one gram?

d.Use your results to calculate the drift speed (i.e., the average net speed) of the electrons in the wire.

e.Due to thermal motion, the electrons at room temperature are randomly traveling to and fro at 1.13

Explanation / Answer

a).

14.0A means 14.0 C of charge per second passing a given point.

14/1.60x10^-19 = 8.75x10^19 electrons per second

Or electron density of 8.75x10^19/(?*(0.425x10^-3)^2) = 1.542x10^26 electron per m^2 per second

B) There are 2.70g/cm^3/27.4g/mol*6.022x10^23molecule... electron/molecule

= 1.68x10^23 electron/cm^3 = 1.68x10^29 electrons/m^3

C) vd = J/(n*q) = 14.0/(?*(0.425x10^-3)^2)/(1.68x10^29*1.6) = 1.03x10^-3m/s

D) we have 1.03x10^-3/1.13x10^5 = 9.11x10^-9

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