   Chapter 17, Problem 9P

Chapter
Section
Textbook Problem

An iron wire has a cross-sectional area of 5.00 × 10−6 m2. Carry out steps (a) through (e) to compute the drift speed of the conduction electrons in the wire. (a) How many kilograms are there in 1 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) If the wire carries a current of 30.0 A, calculate the drift speed of conduction electrons.

(a)

To determine
The mass of 1 mole of iron.

Explanation

Given Info: The area of cross section of iron wire is 5×106m2 .

Explanation:

Formula to calculate the mass from number of moles is,

m=nM

• n is the number of moles of iron,
• m is the mass in kilogram of iron,
• M is the molecular mass of iron,

Substitute 1 mol for n and 55.85gmol-1 for M to find m.

m=(1mol)(55

(b)

To determine
The molar density of iron.

(c)

To determine
The number density of iron using Avogadro number

(d)

To determine
The charge carrier density when there are two conduction electron per atom.

(e)

To determine
The drift speed of conduction electrons

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