To solve this problem we will apply the concepts related to energy conservation. We will start by defining the expressions of the electric potential energy for a given charge (and for the electron). With this we can apply the conservation of kinematic energy. Our values are given as
[tex]V = 80000V[/tex]
The potential energy:
[tex]U = qV[/tex]
Here,
q = Charge
V = Voltage
Or specifically for an electron we can define it as,
[tex]U_e = eV[/tex]
Here,
e = Charge of electron
V = Voltage
Applying the energy conservation equations we have that the kinetic energy must be equivalent to the electric potential energy,
[tex]KE= U_e[/tex]
[tex]\frac{1}{2}mv^2 = qV =e V[/tex]
Here
v = Velocity
m = Mass
Rearranging,
[tex]v^2 = \frac{2eV}{m}[/tex]
Replacing,
[tex]v^2 = \frac{2(1.6*10^{-19})(80000)}{9.1*10^{-31}}[/tex]
[tex]v= 2.81*10^{16}[/tex]
For each electron the velocity is,
[tex]v = 1.68*10^8m/s[/tex]
Therefore the velocity of the electron is [tex]1.68*10^8m/s[/tex]
