An iron wire has a cross-sectional area of 1.31 10-5 m2. Carry out steps (a) thr

Question

An iron wire has a cross-sectional area of 1.31 10-5 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? 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) If the wire carries a current of 15.0 A, calculate the drift speed of conduction electrons. m/s

Explanation / Answer

a) molar mass of Iron, M = 55.8 gram/mol

= 0.0558 kg/mol

b) we know, density of Iron = molar density of Iron = M/density of Iron

= (7860 kg/m^3)/(0.0558 kg/mol)

= 1.408*10^5 mol/m^3

c) number density of iron atoms = 1.408*10^5*6.023*10^23 atoms/m^3

= 8.48*10^28 atoms/m^3

d) electron density, n = 2*8.48*10^28

= 1.70*10^29 electrons/m^3

e) drift speed, vd = I/(A*n*q)

= 15/(1.31*10^-5*1.70*10^29*1.6*10^-19)

= 4.21*10^-5 m/s

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