What should be the rest energy of an electron ?

Options

A. 510 KeV
B. 931 KeV
C. 510 MeV
D. 931 MeV

Explanation

To find the rest energy of an electron, we can use the famous equation from Einstein's theory of relativity:

\[ E = mc^2 \]

Where:
- \( E \) is the rest energy,
- \( m \) is the mass of the electron,
- \( c \) is the speed of light in a vacuum.

### Step-by-Step Solution:

**Step 1: Identify the mass of the electron.**
The mass of the electron is given as:
\[ m = 9.1 \times 10^{-31} \text{ kg} \]

**Step 2: Identify the speed of light.**
The speed of light is:
\[ c = 3 \times 10^8 \text{ m/s} \]

**Step 3: Substitute the values into the equation.**
Using the equation \( E = mc^2 \):
\[ E = (9.1 \times 10^{-31} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]

**Step 4: Calculate \( c^2 \).**
First, calculate \( c^2 \):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]

**Step 5: Substitute \( c^2 \) back into the equation.**
Now substitute \( c^2 \) into the energy equation:
\[ E = 9.1 \times 10^{-31} \times 9 \times 10^{16} \]

**Step 6: Perform the multiplication.**
Calculate the energy:
\[ E = 81.9 \times 10^{-15} \text{ J} \]
\[ E = 8.19 \times 10^{-14} \text{ J} \]

**Step 7: Convert joules to electron volts.**
To convert joules to electron volts, we use the conversion factor \( 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \):
\[ E (\text{eV}) = \frac{E (\text{J})}{1.6 \times 10^{-19}} \]
\[ E = \frac{8.19 \times 10^{-14}}{1.6 \times 10^{-19}} \]

**Step 8: Perform the division.**
Calculating the division gives:
\[ E \approx 5.11875 \times 10^{5} \text{ eV} \]
\[ E \approx 0.511875 \text{ MeV} \]

**Final Result:**
The rest energy of the electron is approximately:
\[ E \approx 0.511 \text{ MeV} \]