The mass of an electron is m, its charge is e and it is accelerated from rest through a potential difference, V. The velocity of electron can be calculated by formula:

Explanation

To find the velocity of an electron that is accelerated from rest through a potential difference \( V \), we can use the relationship between kinetic energy and electric potential energy. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Understand the Energy Conversion**:
When an electron is accelerated through a potential difference \( V \), the electrical energy gained by the electron is converted into kinetic energy. The potential energy gained by the electron is given by:
\[ \text{Potential Energy} = eV \]
where \( e \) is the charge of the electron.

2. **Kinetic Energy Expression**:
The kinetic energy (KE) of the electron when it has been accelerated is given by:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the electron and \( v \) is its velocity.

3. **Set the Energies Equal**:
Since the potential energy is converted into kinetic energy, we can set the two expressions equal to each other:
\[ eV = \frac{1}{2} mv^2 \]

4. **Rearranging for Velocity**:
To find the velocity \( v \), we rearrange the equation:
\[ \frac{1}{2} mv^2 = eV \]
Multiply both sides by 2:
\[ mv^2 = 2eV \]
Now, divide both sides by \( m \):
\[ v^2 = \frac{2eV}{m} \]

5. **Taking the Square Root**:
Finally, take the square root of both sides to solve for \( v \):
\[ v = \sqrt{\frac{2eV}{m}} \]

### Final Answer:
The velocity of the electron after being accelerated through a potential difference \( V \) is given by:
\[ v = \sqrt{\frac{2eV}{m}} \]