A certain mass of hydrogen is changed to helium by the process of fusion. The mass defect in fusion reaction is `0.02866 u`. The energy liberated per `u` is
`("given "1 u=931 MeV)`

Options

A. `2.67` MeV
B. `26.7` MeV
C. `6.675` MeV
D. `13.35` MeV

Answer

To solve the problem, we need to calculate the energy liberated during the fusion of hydrogen into helium using the mass defect provided. Here’s a step-by-step solution:

### Step 1: Understand the mass defect
The mass defect (ΔM) is given as 0.02866 u. This is the amount of mass that is converted into energy during the fusion process.

### Step 2: Use the mass-energy equivalence formula
According to Einstein's mass-energy equivalence principle, the energy (E) released can be calculated using the formula:
\[ E = \Delta M \cdot c^2 \]
However, in nuclear physics, we often use the conversion factor that 1 atomic mass unit (u) corresponds to 931 MeV of energy.

### Step 3: Calculate the energy liberated
To find the energy liberated in MeV, we can use the following equation:
\[ E = \Delta M \cdot (931 \text{ MeV/u}) \]
Substituting the value of ΔM:
\[ E = 0.02866 \text{ u} \cdot 931 \text{ MeV/u} \]

### Step 4: Perform the multiplication
Now, we calculate:
\[ E = 0.02866 \cdot 931 \]
\[ E \approx 26.67 \text{ MeV} \]

### Step 5: Finalize the answer
The energy liberated during the fusion of hydrogen to helium, given the mass defect, is approximately:
\[ E \approx 26.67 \text{ MeV} \]

### Summary of the solution:
The energy liberated per atomic mass unit (u) is calculated using the mass defect and the conversion factor, resulting in approximately 26.67 MeV.

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