Question

An electron enters in higher potential region v2 from lower potential region v1, then its velocity:

Answer 1

Then its Velocity increases due to the Acceleration it will get in the direction of its motion.An Electron has the natural tendency to move from lower potential to higher potential and thus its velocity increases

Answer 2

The correct answer to the question is $\ \sqrt{\frac{2e}{m}(v_{2} -v_{1})}$

CALCULATION:

The higher potential is given as $v_{2}$

The lower potential is given as $v_{1}$

Hence, the potential difference is calculated as $(\ v_{2} -v_{1})$

The kinetic energy gained by the electron due to the potential difference is the product of the charge of electron with the potential difference.

Mathematically kinetic energy K.E = $e(\ v_{2} -v_{1})$  [1]

We are asked to calculate the velocity of electron.

Let the velocity of the electron is V and mass is m.

Hence, the kinetic energy of the electron is calculated as -

                                                         K.E = $\frac{1}{2}mV^2$   [2]

From 1 and 2 we get, $\frac{1}{2}mV^2=\ e(v_{2} -v_{1})$

                                   ⇒  $V^2=\ \frac{2e}{m}(v_{2}-v_{1})$

                                    ⇒ $V=\ \sqrt{\frac{2e}{m}(v_{2} -v_{1})}$  [ans]