If a star can convert all the He nuclei completely into oxygen nuclei. The energy released per oxygen nuclei is (Mass of the helium nucleus is 4.0026 amu and mass of oxygen nucleus is 15.9994 amu)

Options

A. (a) 7.6 MeV
B. (b) 56.12 MeV
C. (c) 10.24 MeV
D. (d) 23.4 MeV

Explanation

To calculate the energy released per oxygen nucleus when helium nuclei are converted into oxygen nuclei, we can follow these steps:

### Step 1: Understand the Reaction
The reaction involves the conversion of two helium nuclei (He) into one oxygen nucleus (O). The reaction can be represented as:
\[ 2 \text{He} \rightarrow \text{O} \]

### Step 2: Determine the Masses
We are given the masses of the helium and oxygen nuclei:
- Mass of helium nucleus (He) = 4.0026 amu
- Mass of oxygen nucleus (O) = 15.9994 amu

### Step 3: Calculate the Total Mass of Helium Nuclei
Since two helium nuclei are involved in the reaction, we calculate the total mass of the helium nuclei:
\[ \text{Total mass of He} = 2 \times \text{Mass of He} = 2 \times 4.0026 \text{ amu} = 8.0052 \text{ amu} \]

### Step 4: Calculate the Change in Mass
The change in mass (Δm) during the reaction is given by the difference between the total mass of the helium nuclei and the mass of the oxygen nucleus:
\[ \Delta m = \text{Total mass of He} - \text{Mass of O} \]
\[ \Delta m = 8.0052 \text{ amu} - 15.9994 \text{ amu} \]
\[ \Delta m = -7.9942 \text{ amu} \]

### Step 5: Convert the Change in Mass to Energy
To find the energy released, we use the mass-energy equivalence principle, where 1 amu corresponds to approximately 931.5 MeV. The energy released (E) can be calculated as:
\[ E = \Delta m \times 931.5 \text{ MeV/amu} \]
Since we are interested in the energy released per oxygen nucleus, we take the absolute value of Δm:
\[ E = 7.9942 \text{ amu} \times 931.5 \text{ MeV/amu} \]

### Step 6: Calculate the Energy
Now we perform the multiplication:
\[ E = 7.9942 \times 931.5 \]
\[ E \approx 7430.6 \text{ MeV} \]

### Step 7: Energy Released Per Oxygen Nucleus
Since the reaction produces one oxygen nucleus from two helium nuclei, the energy released per oxygen nucleus is:
\[ E \approx 7430.6 \text{ MeV} \]

### Final Answer
The energy released per oxygen nucleus is approximately **7430.6 MeV**.

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