In fission of one uranium-235 nucleus, the loss in mass is 0.2 a.m.u. Calculate the energy released.

Answer

To solve the problem of calculating the energy released during the fission of one uranium-235 nucleus with a mass loss of 0.2 amu, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Loss in mass (mass defect) = 0.2 amu

2. **Use Einstein's Mass-Energy Relation:**
- The formula to calculate the energy released (E) is given by:
\[ E = \Delta m \cdot c^2 \]
- Where:
- \( E \) is the energy released,
- \( \Delta m \) is the mass defect,
- \( c \) is the speed of light.

3. **Convert Mass Defect from amu to MeV:**
- The conversion factor from atomic mass units (amu) to energy in MeV is:
\[ 1 \text{ amu} \approx 931.5 \text{ MeV} \]
- Therefore, to find the energy in MeV for a mass defect of 0.2 amu, we can use:
\[ E = \Delta m \cdot 931.5 \text{ MeV} \]

4. **Calculate the Energy Released:**
- Substitute the values into the equation:
\[ E = 0.2 \text{ amu} \cdot 931.5 \text{ MeV/amu} \]
- Performing the multiplication:
\[ E = 0.2 \cdot 931.5 = 186.3 \text{ MeV} \]

5. **Final Result:**
- The energy released in the fission of one uranium-235 nucleus is:
\[ E \approx 186.3 \text{ MeV} \]

### Summary:
The energy released during the fission of one uranium-235 nucleus with a mass loss of 0.2 amu is approximately **186.3 MeV**.

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