Verified Answer :
The time to take 1 mole of electron, with drift velocity \(5.00*10^{-5} m/s\) to flow through a cross section of the wire is \(0.18* 10^{6} s\).
What is drift velocity?
Drift velocity is the average velocity attained by charged particles in a material due to an electric field.
\(v_{d}=\frac{I}{n e A}\)
Where,
\(v_{d}\) = drift velocity
I = current flow
n = free electron density
e = charge of an electron
A = cross sectional area
What is conduction electron?
An electron in the conduction band of a solid, where it is free to move under the influence of an electric field.
What is electron density?
Electron density is a representation of the probability of finding an electron in a specific location around an atom or molecule.
Given data:
The number of electrons is 1 mole = \(6.02 * 10^{23}\)
The diameter of gold wire = 1.2 mm
The drift speed \(v_{d}\) = \(5.00*10^{-5} m/s\)
Number of conduction electrons in gold wire = \(5.90 * 10^{28} m^{-3}\)
Cross sectional area is,
\(A = \frac{\pi d^{2} }{4} \\A = 1.13*10^{-6} m^{2}\)
The number of electrons that flows through the cross-sectional area at the given time t is mathematically represented as
\(N = n Av_{d}t\)
\(6.02 * 10^{23} = 5.90 * 10^{28}*1.13*10^{-6} *5.00*10^{-5}*t\)
\(t = 0.18* 10^{6} s\)
Hence, the time for 1 mole to pass through a cross section of wire is \(0.18*10^{6} s\).
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