Respuesta :
The time to take 1 mole of electron, with drift velocity [tex]5.00*10^{-5} m/s[/tex] to flow through a cross section of the wire is [tex]0.18* 10^{6} s[/tex].
What is drift velocity?
Drift velocity is the average velocity attained by charged particles in a material due to an electric field.
[tex]v_{d}=\frac{I}{n e A}[/tex]
Where,
[tex]v_{d}[/tex] = 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 = [tex]6.02 * 10^{23}[/tex]
The diameter of gold wire = 1.2 mm
The drift speed [tex]v_{d}[/tex] = [tex]5.00*10^{-5} m/s[/tex]
Number of conduction electrons in gold wire = [tex]5.90 * 10^{28} m^{-3}[/tex]
Cross sectional area is,
[tex]A = \frac{\pi d^{2} }{4} \\A = 1.13*10^{-6} m^{2}[/tex]
The number of electrons that flows through the cross-sectional area at the given time t is mathematically represented as
[tex]N = n Av_{d}t[/tex]
[tex]6.02 * 10^{23} = 5.90 * 10^{28}*1.13*10^{-6} *5.00*10^{-5}*t[/tex]
[tex]t = 0.18* 10^{6} s[/tex]
Hence, the time for 1 mole to pass through a cross section of wire is [tex]0.18*10^{6} s[/tex].
To learn more about Drift velocity here
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