A nuclear reaction is accompanied by loss of mass equivalent to 0.01864 amu. Energy liberated is:

Options

A. 931 MeV
B. 186.6 MeV
C. 17.36 MeV
D. 460 MeV

Answer

To solve the problem of calculating the energy liberated from a nuclear reaction that has a mass loss of 0.01864 amu, we can use Einstein's mass-energy equivalence principle, which is given by the equation:

\[ E = \Delta m \cdot c^2 \]

However, in this case, we will use the known conversion factor that 1 atomic mass unit (amu) is equivalent to 931 MeV (mega-electron volts) of energy.

### Step-by-Step Solution:

1. **Identify the mass loss**:
The mass loss in the nuclear reaction is given as:
\[ \Delta m = 0.01864 \, \text{amu} \]

2. **Use the conversion factor**:
We know that 1 amu is equivalent to 931 MeV. Therefore, we can express the energy equivalent of the mass loss as:
\[ E = \Delta m \times \text{(energy equivalent of 1 amu)} \]
Substituting the values:
\[ E = 0.01864 \, \text{amu} \times 931 \, \text{MeV/amu} \]

3. **Perform the multiplication**:
Now, we calculate the energy:
\[ E = 0.01864 \times 931 \]
Performing the calculation:
\[ E \approx 17.36 \, \text{MeV} \]

4. **Final Result**:
The energy liberated in the nuclear reaction is approximately:
\[ E \approx 17.36 \, \text{MeV} \]