What is the equivalent energy of a 10 mg mass ?

Answer

To find the equivalent energy of a 10 mg mass, we can use Einstein's mass-energy equivalence formula, which is given by:

\[ E = mc^2 \]

where:
- \( E \) is the energy,
- \( m \) is the mass,
- \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) m/s).

### Step-by-Step Solution:

1. **Convert the mass from mg to kg**:
\[ 10 \text{ mg} = 10 \times 10^{-3} \text{ g} = 10 \times 10^{-6} \text{ kg} \]

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

3. **Substitute the values into the mass-energy equivalence formula**:
\[ E = mc^2 = (10 \times 10^{-6} \text{ kg}) \times (3 \times 10^8 \text{ m/s})^2 \]

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

5. **Now calculate the energy \( E \)**:
\[ E = 10 \times 10^{-6} \text{ kg} \times 9 \times 10^{16} \text{ m}^2/\text{s}^2 \]
\[ E = 90 \times 10^{10} \text{ kg m}^2/\text{s}^2 = 9 \times 10^{11} \text{ J} \]

6. **Convert the energy from Joules to electron volts**:
\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \]
\[ E = \frac{9 \times 10^{11} \text{ J}}{1.6 \times 10^{-19} \text{ J/eV}} = \frac{9 \times 10^{11}}{1.6 \times 10^{-19}} \text{ eV} \]
\[ E \approx 5.625 \times 10^{30} \text{ eV} \approx 5 \times 10^{30} \text{ eV} \]

### Final Answer:
The equivalent energy of a 10 mg mass is approximately \( 9 \times 10^{11} \) Joules or \( 5 \times 10^{30} \) electron volts.