The mass of an electron is m, charge is e and it is accelerated form rest through a potential difference of V volts. The velocity acquired by electron will be :

Options

A. `sqrt(V/m)`
B. `sqrt((eV)/m)`
C. `sqrt((2eV)/m)`
D. zero

Answer

To find the velocity acquired by an electron when it is accelerated from rest through a potential difference of V volts, we can follow these steps:

### Step 1: Understand the relationship between work done and kinetic energy
When an electron is accelerated through a potential difference, it gains kinetic energy. The work done on the electron by the electric field is equal to the charge of the electron multiplied by the potential difference (V).

**Hint:** Remember that work done (W) is equal to charge (Q) times potential difference (V).

### Step 2: Write the equation for kinetic energy
The kinetic energy (KE) acquired by the electron can be expressed as:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the electron and \( v \) is its final velocity.

**Hint:** Kinetic energy is related to mass and the square of velocity.

### Step 3: Set the work done equal to the kinetic energy
Since the work done on the electron is equal to the kinetic energy it acquires, we can write:
\[ eV = \frac{1}{2} mv^2 \]
where \( e \) is the charge of the electron and \( V \) is the potential difference.

**Hint:** Equate the work done to the kinetic energy to find the relationship between potential difference and velocity.

### Step 4: Rearrange the equation to solve for velocity
From the equation \( eV = \frac{1}{2} mv^2 \), we can rearrange it to solve for \( v^2 \):
\[ mv^2 = 2eV \]
\[ v^2 = \frac{2eV}{m} \]

**Hint:** Isolate \( v^2 \) to express it in terms of the other variables.

### Step 5: Take the square root to find velocity
Now, take the square root of both sides to find the velocity \( v \):
\[ v = \sqrt{\frac{2eV}{m}} \]

**Hint:** Remember that taking the square root gives you the final expression for velocity.

### Final Result
The velocity acquired by the electron when accelerated through a potential difference of \( V \) volts is:
\[ v = \sqrt{\frac{2eV}{m}} \]