When a proton is accelerated through `1 V`, then its kinetic energy will be

Options

A. 1 eV
B. 13.6 eV
C. 1840 eV
D. 0.54 eV

Answer

To find the kinetic energy gained by a proton when it is accelerated through a potential difference of 1 volt, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between electric potential and kinetic energy**:
When a charged particle, such as a proton, is accelerated through a potential difference (V), it gains kinetic energy (KE). The relationship is given by the equation:
\[ KE = q \cdot V \]
where \( q \) is the charge of the particle and \( V \) is the potential difference.

2. **Identify the charge of the proton**:
The charge of a proton is equal to the elementary charge, which is:
\[ q = 1.6 \times 10^{-19} \, \text{C} \]

3. **Substitute the values into the equation**:
Given that the potential difference \( V = 1 \, \text{V} \), we can substitute the values into the kinetic energy equation:
\[ KE = (1.6 \times 10^{-19} \, \text{C}) \cdot (1 \, \text{V}) \]

4. **Calculate the kinetic energy**:
Since \( 1 \, \text{V} \) is equivalent to \( 1 \, \text{J/C} \), we can rewrite the equation as:
\[ KE = 1.6 \times 10^{-19} \, \text{J} \]

5. **Final answer**:
Therefore, the kinetic energy gained by the proton when it is accelerated through a potential difference of 1 volt is:
\[ KE = 1.6 \times 10^{-19} \, \text{J} \]