If a free electron moves through a potential difference of 1 kV, then the energy gained by the electron is given by

Options

A. `1.6xx10^(-19)J`
B. `1.6xx10^(-16)J`
C. `1xx10^(-19)J`
D. `1xx10^(-16)J`

Explanation

To solve the problem of finding the energy gained by a free electron moving through a potential difference of 1 kV, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between energy, charge, and potential difference**:
The energy (E) gained by a charge (Q) when it moves through a potential difference (V) is given by the formula:
\[ E = Q \times V \]

2. **Identify the charge of the electron**:
The charge of a free electron (Q) is approximately:
\[ Q = 1.6 \times 10^{-19} \text{ C} \]

3. **Convert the potential difference from kilovolts to volts**:
Since the potential difference is given as 1 kV, we convert it to volts:
\[ V = 1 \text{ kV} = 1000 \text{ V} = 10^3 \text{ V} \]

4. **Substitute the values into the energy formula**:
Now, we can substitute the values of Q and V into the energy formula:
\[ E = (1.6 \times 10^{-19} \text{ C}) \times (10^3 \text{ V}) \]

5. **Calculate the energy**:
Performing the multiplication:
\[ E = 1.6 \times 10^{-19} \times 10^3 = 1.6 \times 10^{-16} \text{ J} \]

6. **Final Result**:
The energy gained by the electron when it moves through a potential difference of 1 kV is:
\[ E = 1.6 \times 10^{-16} \text{ J} \]