In fission,the percentage of mass converted into energy is about

Options

A. `94%`
B. `1%`
C. `0.1%`
D. `0.01%`

Explanation

To find the percentage of mass converted into energy during nuclear fission, we can follow these steps:

### Step 1: Understand the Binding Energy
In nuclear fission, a heavy nucleus splits into two smaller nuclei. The binding energy per nucleon of the products is higher than that of the reactants. This means that energy is released during the fission process.

### Step 2: Identify the Binding Energies
From the information given:
- Binding energy per nucleon of products = 8.5 MeV
- Binding energy per nucleon of reactants = 7.6 MeV

### Step 3: Calculate the Change in Binding Energy
The change in binding energy (ΔE) can be calculated as:
\[ \Delta E = \text{Binding energy of products} - \text{Binding energy of reactants} \]
Substituting the values:
\[ \Delta E = 8.5 \, \text{MeV} - 7.6 \, \text{MeV} = 0.9 \, \text{MeV} \]

### Step 4: Convert Energy Change to Mass Change
Using Einstein's equation \(E = mc^2\), we can convert the energy change into mass change. The conversion factor is \(931 \, \text{MeV/c}^2\) per atomic mass unit (u):
\[ \Delta M = \frac{\Delta E}{931 \, \text{MeV/u}} = \frac{0.9 \, \text{MeV}}{931 \, \text{MeV/u}} \approx 0.000966 \, \text{u} \]

### Step 5: Calculate the Percentage Change in Mass
To find the percentage of mass converted into energy, we can express the change in mass as a percentage of the original mass. Assuming the original mass is approximately 1 u, the percentage change in mass is:
\[ \text{Percentage change in mass} = \left(\frac{\Delta M}{\text{Original mass}}\right) \times 100\% \]
Substituting the values:
\[ \text{Percentage change in mass} = \left(0.000966 \, \text{u} \div 1 \, \text{u}\right) \times 100\% \approx 0.0966\% \]
This can be approximated to:
\[ \text{Percentage change in mass} \approx 0.1\% \]

### Conclusion
Thus, the percentage of mass converted into energy during fission is approximately **0.1%**.

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