An iron wire has a cross-sectional area equal to 1.45 10-5 m2. Carry out the fol

Question

An iron wire has a cross-sectional area equal to 1.45 10-5 m2. Carry out the following steps to determine the drift speed of the conduction electrons in the wire if it carries a current of 25.0 A. (a) How many kilograms are there in 1.00 mole of iron? (b) Starting with the density of iron and the result of part (a), compute the molar density of iron (the number of moles of iron per cubic meter). (c) Calculate the number density of iron atoms using Avogadro's number. (d) Obtain the number density of conduction electrons given that there are two conduction electrons per iron atom. (e) Calculate the drift speed of conduction electrons in this wire.

Explanation / Answer

a) 1 mole = 56 g of Iron [Gram Molecular weight of Iron]

1 mole = 0.056 Kg

b) Density of iron = 7870 Kg/m3

Molar density = Density / Molar mass = 7870 / 0.056 = 1.405 *105 moles/m3

c) Number density = Molar density * NA = 8.463 * 1028 atoms

d) Conduction electron, n = Number density * 2 = 1.693 *1029 e-

e) I = n e A Vd

Vd = I / neA = 3.8 * 10-4 m/s

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