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 of a proton accelerated through a potential difference of one million volts (1 MV), we can use the formula for kinetic energy gained by a charged particle in an electric field:

\[ KE = q \cdot V \]

Where:
- \( KE \) is the kinetic energy,
- \( q \) is the charge of the particle,
- \( V \) is the potential difference.

### Step-by-Step Solution:

1. **Identify the charge of the proton**:
The charge \( q \) of a proton is given as \( +1.6 \times 10^{-19} \) C.

2. **Identify the potential difference**:
The potential difference \( V \) is given as 1 million volts, which is \( 10^6 \) V.

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

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

5. **Final result**:
The kinetic energy of the proton after being accelerated through a potential difference of 1 million volts is:
\[ KE = 1.6 \times 10^{-13} \, \text{J} \]