An iron wire has a cross-sectional area equal to 2.50 10 6 m 2 . Carry out the f

Question

An iron wire has a cross-sectional area equal to 2.50 106 m2. Carry out the following steps to determine the drift speed of the conduction electrons in the wire if it carries a current of25.0 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

part a )

molar mass of irom = 55.8 g/mol

in 1 mol = 5.58 x 10^-2 kg/mol

part b )

density of iron = 7.86 x 10^3 kg/m^3

molar density = rho/M = (7.86 x 10^3)/(5.58 x 10^-2) = 1.41 x 10^5 mol/m^3

part c )

density of atoms = Na*(molar density )

= 6.023 x 10^23 * 1.41 x 10^5 = 8.49 x 10^28 atoms/m^3

part d )

With two conduction electrons per iron atom, the density of charge carriers is

n = (charge carreies/atom)(denstiy of aoms)

n = 2 * 8.49 x 10^28 = 1.70 x 10^29 electrons/m^3

part d )

Vd = I/nqA

I = 25

A = 2.5 x 10^-6

q = 1.6 x 10^-19

Vd = 3.676 x 10^-4 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.