Helium nuclei combine to form an oxygen nucleus. The energy released in the reaction is if `m_(O)=15.9994 "amu"` and `m_(He)=4.0026 "amu"`

Options

A. `10.24 Me V`
B. `0 Me V`
C. `5.24 Me V`
D. `4 Me V`

Explanation

To solve the problem of calculating the energy released when helium nuclei combine to form an oxygen nucleus, we will follow these steps:

### Step 1: Determine the change in mass (Δm)
The reaction involves 4 helium nuclei combining to form 1 oxygen nucleus. The change in mass can be calculated using the formula:

\[ \Delta m = 4 \cdot m_{He} - m_{O} \]

Where:
- \( m_{He} = 4.0026 \, \text{amu} \) (mass of helium nucleus)
- \( m_{O} = 15.9994 \, \text{amu} \) (mass of oxygen nucleus)

### Step 2: Substitute the values into the equation
Substituting the values into the equation gives:

\[ \Delta m = 4 \cdot 4.0026 \, \text{amu} - 15.9994 \, \text{amu} \]

### Step 3: Calculate Δm
Now we perform the calculation:

\[ \Delta m = 16.0104 \, \text{amu} - 15.9994 \, \text{amu} = 0.0110 \, \text{amu} \]

### Step 4: Convert Δm to energy (E)
Using Einstein's mass-energy equivalence principle, we can convert the change in mass to energy using the formula:

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

Where \( c \) (speed of light) is approximately \( 3 \times 10^8 \, \text{m/s} \). To convert from amu to MeV, we use the conversion factor:

\[ 1 \, \text{amu} \approx 931.5 \, \text{MeV/c}^2 \]

Thus, the energy released can be calculated as:

\[ E = 0.0110 \, \text{amu} \cdot 931.5 \, \text{MeV/amu} \approx 10.25 \, \text{MeV} \]

### Step 5: Calculate the binding energy per nucleon
To find the binding energy per nucleon, we divide the total energy released by the number of nucleons in the oxygen nucleus. The oxygen nucleus has 16 nucleons (8 protons and 8 neutrons).

\[ \text{Binding Energy per Nucleon} = \frac{E}{N} = \frac{10.25 \, \text{MeV}}{16} \approx 0.640625 \, \text{MeV} \]

### Final Answer
The energy released in the reaction is approximately **10.25 MeV**.

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