An iron wire has a cross-sectional area equal to 4.00 10-6 m2. Carry out the fol

Question

An iron wire has a cross-sectional area equal to 4.00 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 9.0 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

An iron wire has a cross-sectional area equal to 4.00 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 9.0 A.

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

The molar mass of Iron is 0.05585 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

= 7874 Kg/m3

1/0.05585 * 7874 = 140985 mol/m3

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

140985* 6.022e23 = 8.49012E28 atoms/m3

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

1.69802e29 electrons/m3

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

v = i/nqA = 9/(1.69802e29*1.6e-19*4e-6) = 8.282e-5 m/s

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