The energy equivalent of one atomic mass unit is

Options

A. `1.6xx10^(-19) J`
B. `6.02xx10^(23) J`
C. `931` MeV
D. `9.31` MeV

Answer

To find the energy equivalent of one atomic mass unit (amu), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Atomic Mass Unit (amu)**:
- One atomic mass unit (1 amu) is defined as \( 1.656 \times 10^{-27} \) kg.

2. **Use Einstein's Mass-Energy Equivalence**:
- According to Einstein's equation, the energy equivalent of a mass defect can be calculated using the formula:
\[ E = \Delta m \cdot c^2 \]
- Here, \( \Delta m \) is the mass in kilograms, and \( c \) is the speed of light, which is approximately \( 3 \times 10^8 \) m/s.

3. **Substitute the Values**:
- Substitute \( \Delta m = 1.656 \times 10^{-27} \) kg and \( c = 3 \times 10^8 \) m/s into the equation:
\[ E = (1.656 \times 10^{-27} \text{ kg}) \cdot (3 \times 10^8 \text{ m/s})^2 \]

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

5. **Calculate the Energy in Joules**:
- Now, substitute \( c^2 \) back into the energy equation:
\[ E = 1.656 \times 10^{-27} \cdot 9 \times 10^{16} = 1.4904 \times 10^{-10} \text{ Joules} \]

6. **Convert Joules to Electron Volts**:
- To convert energy from Joules to electron volts, use the conversion factor \( 1 \text{ eV} = 1.6 \times 10^{-19} \text{ Joules} \):
\[ E \text{ (in eV)} = \frac{1.4904 \times 10^{-10}}{1.6 \times 10^{-19}} \approx 9.315 \times 10^8 \text{ eV} = 931.5 \text{ MeV} \]

7. **Final Result**:
- Therefore, the energy equivalent of one atomic mass unit is approximately \( 931.5 \text{ MeV} \).