# An electron moves from one plate to another across which there is a potential difference of 2000...

## Question:

An electron moves from one plate to another across which there is a potential difference of 2000 V.

Find the speed with which the electron strikes the positive plate.

## Potentials and Energy:

When an electron or other charged particle travels through a region of a potential difference, the particle gains a potential energy. Now by the conservation of energy, this potential energy is converted to kinetic energy once the particle moves under the potential. The potential difference that is used here is called the "accelerating voltage".

Given:

• {eq}\displaystyle V = 2000\ V {/eq} is the potential difference

When the electron is accelerated through the potential difference, it gains an energy equal to:

{eq}\displaystyle E = qV {/eq}

Now at the max speed that it can achieve through the potential difference, this potential energy can be converted entirely to kinetic energy. We can thus equate these two:

{eq}\displaystyle qV = \frac{1}{2} mv^2 {/eq}

We now isolate the speed:

{eq}\displaystyle v = \sqrt{\frac{2qV}{m}} {/eq}

We substitute here (we use the charge and the mass for an electron):

{eq}\displaystyle v = \sqrt{\frac{2(1.602\ \times\ 10^{-19}\ C)(2000\ V)}{9.109\ \times\ 10^{-31}\ kg}} {/eq}

We will thus get;

{eq}\displaystyle \boxed{v = 2.65\ \times\ 10^7\ m/s} {/eq} 