An Iron wire has a cross-sectional area of 5.00 x 10^-6 m^2. Carry out steps (a)

Question

An Iron wire has a cross-sectional area of 5.00 x 10^-6 m^2. Carry out steps (a) through (e) to compute the drift speed of the conduction electrons in the wire. a) How many kilogram 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 sing Avogadro's number. d) Obtain the number density of conduction electrons given that there are two conduction electron per iron atom. e) If the wire carries a current of 30.00 A, calcualte the drift speed of conduction electrons.

Explanation / Answer

a) a mole of iron is 55.847g, so 1 kg has 17.9 moles of iron b) density of iron is 7.874 g/cc m^3 is 100cm*100cm*100cm so a million cc's density times 1,000,000 = 7,874 kg/m^3 molar density = (17.9 moles/ kg) * (7,874 kg/m^3) = 149,992 moles/m^3 c) 6.022 x 10^23 so (6.022 x 10^23atoms/mole)*149,992 moles/m^3 = 8.49 x 10^28 atoms/m^3 d) electrons = 2*atoms electron density = 1.70 x 10^29 e-/m^3 e) 30 A cross sectional area is 5.00 x 10^-6 m^-2 i = current A = cross sectional area j = i/A = current density = 6,000,000 A/m^2 velocity = j/ne n = number density e = charge each one has = 1.6 x 10^-19 C/electron v = 6,000,000 A/m^2/[1.70E+29e-'s/m^3*1.6E-19 C/e-] = 2.21 E-04 m/s v = .221 mm/s quite slow

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