Question

In the microscopic view of electrical conduction in a copper wire, electrons are accelerated by an electric field and then collide with metal atoms after traveling about4.2×10−8m.
If an electron begins from rest and is accelerated by a field of 0.080 N/C, what is its speed when it collides with a metal atom?

Answer 1

Answer:

34.35464 m/s

Explanation:

q = Charge of electron = $1.6\times 10^{-19}\ C$

E = Electric field = 0.08 N/C

s = Displacement = $4.2\times 10^{-8}\ m$

m = Mass of electron = $9.11\times 10^{-31}\ kg$

Electrical force is given by

$F=qE$

Work done is given by

$W=Fs\\\Rightarrow W=qEs$

Work done is also given by the kinetic energy

$\dfrac{1}{2}mv^2=qEs\\\Rightarrow v=\sqrt{\dfrac{2qEs}{m}}\\\Rightarrow v=\sqrt{\dfrac{2\times 1.6\times 10^{-19}\times 0.08\times 4.2\times 10^{-8}}{9.11\times 10^{-31}}}\\\Rightarrow v=34.35464\ m/s$

The velocity of the electron is 34.35464 m/s