Energy equal to the mass of one electrons is

Options

A. `8.2 xx 10^(-7)` ergs
B. `9.2 xx 10^(-8)` erg
C. `8.2 xx 10^(-10)` erg
D. `4.1 xx 10^(-8)` erg

Answer

To find the energy equivalent to the mass of one electron, we can use Einstein's mass-energy equivalence formula:

### Step-by-Step Solution:

1. **Identify the formula**:
The energy (E) is given by the equation:
\[ E = mc^2 \]
where:
- \( m \) is the mass of the electron,
- \( c \) is the speed of light in a vacuum.

2. **Determine the mass of the electron**:
The mass of one electron is:
\[ m = 9.1 \times 10^{-31} \text{ kg} \]

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

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

5. **Substitute values into the energy equation**:
Now substitute the values of \( m \) and \( c^2 \) into the equation:
\[ E = (9.1 \times 10^{-31} \text{ kg}) \times (9 \times 10^{16} \text{ m}^2/\text{s}^2) \]

6. **Perform the multiplication**:
\[ E = 81.9 \times 10^{-15} \text{ kg m}^2/\text{s}^2 = 81.9 \times 10^{-15} \text{ Joules} \]

7. **Convert Joules to ergs**:
Since \( 1 \text{ Joule} = 10^7 \text{ ergs} \), we convert the energy from Joules to ergs:
\[ E = 81.9 \times 10^{-15} \text{ Joules} \times 10^7 \text{ ergs/Joule} = 8.19 \times 10^{-8} \text{ ergs} \]

8. **Final answer**:
The energy equivalent to the mass of one electron is approximately:
\[ E \approx 8.2 \times 10^{-8} \text{ ergs} \]

### Summary:
The energy equivalent to the mass of one electron is \( 8.2 \times 10^{-8} \text{ ergs} \).

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