Calculate the binding energy per nucleon for `C^(12)` Masses of proton and neutron are `1.0078` and 1.0087, respectively.
`(m_(u)=931MeV)`

Explanation

To calculate the binding energy per nucleon for Carbon-12 (C-12), we can follow these steps:

### Step 1: Identify the number of protons and neutrons in C-12
Carbon-12 has:
- Number of protons (Z) = 6
- Number of neutrons (N) = 6

### Step 2: Calculate the total mass of protons and neutrons
Using the given masses:
- Mass of one proton (m_p) = 1.0078 u
- Mass of one neutron (m_n) = 1.0087 u

Total mass of protons = Number of protons × Mass of one proton
\[ \text{Total mass of protons} = 6 \times 1.0078 = 6.0468 \, \text{u} \]

Total mass of neutrons = Number of neutrons × Mass of one neutron
\[ \text{Total mass of neutrons} = 6 \times 1.0087 = 6.0522 \, \text{u} \]

### Step 3: Calculate the combined mass of protons and neutrons
\[ \text{Total mass} = \text{Total mass of protons} + \text{Total mass of neutrons} \]
\[ \text{Total mass} = 6.0468 \, \text{u} + 6.0522 \, \text{u} = 12.099 \, \text{u} \]

### Step 4: Calculate the mass defect (Δm)
The mass defect is the difference between the total mass of the separate nucleons and the actual mass of the nucleus.
\[ \Delta m = \text{Total mass} - \text{Actual mass of C-12} \]
\[ \Delta m = 12.099 \, \text{u} - 12 \, \text{u} = 0.099 \, \text{u} \]

### Step 5: Convert the mass defect to energy (binding energy)
Using the conversion factor \(1 \, \text{u} = 931 \, \text{MeV}\):
\[ \text{Binding Energy} = \Delta m \times 931 \, \text{MeV} \]
\[ \text{Binding Energy} = 0.099 \, \text{u} \times 931 \, \text{MeV} = 92.199 \, \text{MeV} \]

### Step 6: Calculate the binding energy per nucleon
The total number of nucleons in C-12 is:
\[ \text{Total nucleons} = \text{Number of protons} + \text{Number of neutrons} = 6 + 6 = 12 \]
\[ \text{Binding Energy per Nucleon} = \frac{\text{Total Binding Energy}}{\text{Total Nucleons}} = \frac{92.199 \, \text{MeV}}{12} \approx 7.68325 \, \text{MeV} \]

### Final Answer
The binding energy per nucleon for Carbon-12 is approximately \(7.68 \, \text{MeV}\).

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