Gold has one conduction electron per atom. Its density is 19.3 gr/cm^3, molar ma

Question

Gold has one conduction electron per atom. Its density is 19.3 gr/cm^3, molar mass is 197 gr/mole, and resistivity is 2.4 x 10^-8...

5. Gold has one conduction electron per atom. Its density is 19.3 gr/cm', molar mass is 197 gr/mole and resistivity is 2.4 × 10-8 m. A gold wire with length of 155 cm and 0.247 mm diameter has a potential difference of 3 volts applied across its endpoints. Determine the following: a) The Electric Field E in the wire: b) The concentration n: e) The drift speed va of the electrons in the wire: d) The conduction electron collision frequency f rn

Explanation / Answer

(1)

E = V/L = 3/1.55 = 1.93 V/m

(2)

number of moles in m^3 = density/ molar mass

number of atoms = number of moles *NA

NA = avagadro number

n = (19.3*10^6*6.023*10^23)/(197)

n = 5.91*10^23

(3)

current = I = V/R = VA/rhoL = (V*pi*r^2)/(rho*L)

I = (3*pi*(0.1235*10^-3)^2)/(2.48*10^-8*1.55)

I = 3.86 A

v = I/neA = (V*A)/(n*e*A*rho*L) = V/(n*e*rho*L)

drift speed = v = 3/(5.1*10^28*1.6*10^-19*2.4*10^-8*1.55)

drift speed = v = 0.0098 m/s

(d)

f = 1/t = v/L = 0.0098/1.55 = 0.00632 Hz

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