A proton has a mass 1.67 `xx 10^(-27)` kg and charge `+ 1.6 xx 10^(-19)`C. If the proton is accelerated through a potential difference of million volts, then the kinetic energy is

Options

A. `1.6 xx 10^(-15)` J
B. `1.6 xx 10^(-13)` J
C. `1.6 xx 10^(-21)` J
D. `3.2 xx 10^(-13)`J

Answer

To find the kinetic energy gained by a proton when it is accelerated through a potential difference of one million volts, we can use the relationship between electric potential energy and kinetic energy.

### Step-by-Step Solution:

1. **Understand the relationship between potential difference and kinetic energy**:
When a charged particle (like a proton) is accelerated through a potential difference (V), it gains kinetic energy (KE) equal to the work done on it by the electric field. The formula for this is:
\[ KE = q \cdot V \]
where \( q \) is the charge of the particle and \( V \) is the potential difference.

2. **Identify the values**:
- Charge of the proton, \( q = 1.6 \times 10^{-19} \) C
- Potential difference, \( V = 1,000,000 \) V (which is \( 10^6 \) V)

3. **Substitute the values into the formula**:
\[ KE = (1.6 \times 10^{-19} \, \text{C}) \cdot (10^6 \, \text{V}) \]

4. **Calculate the kinetic energy**:
\[ KE = 1.6 \times 10^{-19} \times 10^6 = 1.6 \times 10^{-13} \, \text{J} \]

5. **Final answer**:
The kinetic energy gained by the proton after being accelerated through a potential difference of one million volts is:
\[ KE = 1.6 \times 10^{-13} \, \text{J} \]

### Conclusion:
Thus, the kinetic energy of the proton is \( 1.6 \times 10^{-13} \, \text{J} \).