An iron wire has a cross-sectional area equal to 3.50 10-6 m2. Carry out the fol

Question

An iron wire has a cross-sectional area equal to 3.50 10-6 m2. Carry out the following steps to determine the drift speed of the conduction electrons in the wire if it carries a current of 36.0 A.

(a) How many kilograms are there in 1.00 mole of iron?
____?kg/mol

(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).
____?mol/m3

(c) Calculate the number density of iron atoms using Avogadro's number.
___?atoms/m3

(d) Obtain the number density of conduction electrons given that there are two conduction electrons per iron atom.
____?electrons/m3

(e) Calculate the drift speed of conduction electrons in this wire.
____?m/s

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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