Question

Compute the velocity of an electron that has been accelerated through a difference of potential of 100 volts. express your answer in meters per second

Answer 1

The velocity of an electron that has been accelerated through a difference of potential of 100 volts will be 5.93 * $10^{6}$ m/s

Electrons move because they get pushed by some external force. There are several energy sources that can force electrons to move. Voltage is the amount of push or pressure that is being applied to the electrons.

By conservation of energy, the kinetic energy has to equal the change in potential energy, so KE=q*V. The energy of the electron in electron-volts is numerically the same as the voltage between the plates.

given

charge of electron = 1.6 × $10^{-19}$ C

mass of electron  = 9.1 × $10^{-31}$ kg

Force in an electric field = q*E

potential energy is stored in the form of work done

potential energy = work done = Force * displacement

                                                   = q * (E * d)  

                                                   = q * (V) = 1.6 × $10^{-19}$ * 100

stored potential energy = kinetic energy in electric field

kinetic energy = 1/2 * m * $v^{2}$

                        = 1/2 *  9.1 × $10^{-31}$ *  $v^{2}$

equation both the equations

1/2 *  9.1 × $10^{-31}$ *  $v^{2}$ = 1.6 × $10^{-17}$

$v^{2}$ = 0.352 * $10^{14}$ m/s

$v^{2}$ = 35.2 * $10^{12}$

    = 5.93 * $10^{6}$ m/s

To learn more about  kinetic energy in electric field  here

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