Calculate the binding energy and binding energy per nucleon (in MeV) of a nitrogen nucleus (⁷N₁₄) from the following data:
Mass of proton = 1.00783 u
Mass of neutron = 1.00867 u
Mass of nitrogen nucleus = 14.00307 u

To calculate the binding energy and binding energy per nucleon of a nitrogen nucleus \((^{14}_7\text{N})\), we follow these steps:

### Step 1: Calculate the mass defect
The mass defect is the difference between the total mass of the nucleons (protons and neutrons) and the actual mass of the nucleus.

1. **Number of protons** in nitrogen (\(Z\)): 7
2. **Number of neutrons** (\(N\)): 14 - 7 = 7
3. **Mass of protons**:
\[
\text{Total mass of protons} = 7 \times 1.00783 \, \text{u} = 7.05481 \, \text{u}
\]
4. **Mass of neutrons**:
\[
\text{Total mass of neutrons} = 7 \times 1.00867 \, \text{u} = 7.06069 \, \text{u}
\]
5. **Total mass of nucleons**:
\[
\text{Total mass of nucleons} = 7.05481 \, \text{u} + 7.06069 \, \text{u} = 14.11550 \, \text{u}
\]
6. **Mass defect**:
\[
\Delta m = \text{Total mass of nucleons} - \text{Mass of nitrogen nucleus}
\]
\[
\Delta m = 14.11550 \, \text{u} - 14.00307 \, \text{u} = 0.11243 \, \text{u}
\]

### Step 2: Convert the mass defect to energy
To convert the mass defect into energy, use Einstein's equation:
\[
E = \Delta m \times c^2
\]
Where \(1 \, \text{u} = 931.5 \, \text{MeV/c}^2\).

1. **Binding energy**:
\[
E = 0.11243 \, \text{u} \times 931.5 \, \text{MeV/u}
\]
\[
E = 104.69 \, \text{MeV}
\]

### Step 3: Calculate binding energy per nucleon
The binding energy per nucleon is the total binding energy divided by the number of nucleons.

1. **Number of nucleons**: 14
2. **Binding energy per nucleon**:
\[
\text{Binding energy per nucleon} = \frac{E}{\text{Number of nucleons}}
\]
\[
\text{Binding energy per nucleon} = \frac{104.69 \, \text{MeV}}{14}
\]
\[
\text{Binding energy per nucleon} = 7.48 \, \text{MeV}
\]

### Final Answer
- Binding energy: 104.69 MeV
- Binding energy per nucleon: 7.48 MeV