27 P024 An Iiron wire has a cross sectional area equal to 1.40 x 1o- m2, Carry o

Question

27 P024 An Iiron wire has a cross sectional area equal to 1.40 x 1o- m2, Carry out the following steps to determine the dift sped of the conduction elecdrons in the wi'e I E Caiuat SA (a) How many kilograms are there in 1.00 mole of iron? ko/mol (b) Starting with the density of iron and the result of part (o), compute the molar density of iron (the number of moles of ron ger (c) Cakculate the number density of iron atoms using Avogadro's number (d) Obtain the number density of conduction electrons given that there ar atoms/m e two conduction electrens per iron atfom electrons/m (e) Calculate the drift speed of conduction electrons in this wire. Need Help?

Explanation / Answer

Given,

A = 1.4 x 10^-5 m^2

a)The molar mass of iron is 55.8

This implies that 1 mol of iron has 55.8 g so

M = 55.8 x 10^-3 kg/mol

Hence, M = 0.0558 kg/mol

b)density of iron = 7870 kg/m^3

volume = 0.0558/7870 = 7.09 x 10^-6 m^3

molar density = 1 mol/7.09 x 10^-6 = 1.41 x 10^5 mol/m^3

Hence, molar density = 1.41 x 10^5 mol/m^3

c)one mol = 6.023 x 10^23

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

Hence, number density = 8.49 x 10^28 atoms/m^3

d)there are 2 electrons per atom, so number density will be:

N = 2 x 8.49 x 10^28 atoms/m^3 = 1.69 x 10^29 electrons/m^3

Hence, N = 1.69 x 10^29 electrons/m^3

e)Drift speed is given by:

Vd = I/N e A

(the value of I from the question is not visible, as its blur at the right end.Pls put in the value of current in comment for a complete solution)

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