Obtain the binding energy of a nitrogen nucleus from the following data:
`m_H=1.00783u`,m_N=1.00867u`,m(`_7^14N)=14.00307u`
Give your answer in units of MeV. [Remember `1u=931.5MeV//c^2`]

Explanation

To find the binding energy of the nitrogen nucleus, we can follow these steps:

### Step 1: Identify the parameters
- The mass of a proton (hydrogen nucleus) \( m_H = 1.00783 \, u \)
- The mass of a neutron \( m_N = 1.00867 \, u \)
- The mass of the nitrogen nucleus \( m(^{14}_7N) = 14.00307 \, u \)
- The atomic number of nitrogen \( Z = 7 \) (number of protons)
- The mass number of nitrogen \( A = 14 \) (total number of nucleons)

### Step 2: Calculate the total mass of the constituent nucleons
The total mass of the nucleons (protons and neutrons) in the nitrogen nucleus can be calculated as follows:

\[ \text{Total mass} = Z \cdot m_H + (A - Z) \cdot m_N \]

Substituting the values:

\[ \text{Total mass} = 7 \cdot 1.00783 \, u + (14 - 7) \cdot 1.00867 \, u \]

Calculating this step-by-step:

1. Calculate the mass contribution from protons:
\[ 7 \cdot 1.00783 = 7.05481 \, u \]

2. Calculate the mass contribution from neutrons:
\[ 7 \cdot 1.00867 = 7.06069 \, u \]

3. Add both contributions:
\[ \text{Total mass} = 7.05481 \, u + 7.06069 \, u = 14.1155 \, u \]

### Step 3: Calculate the mass defect
The mass defect \( \Delta m \) is the difference between the total mass of the nucleons and the actual mass of the nitrogen nucleus:

\[ \Delta m = \text{Total mass} - m(^{14}_7N) \]

Substituting the values:

\[ \Delta m = 14.1155 \, u - 14.00307 \, u = 0.11243 \, u \]

### Step 4: Convert mass defect to energy
Using the conversion factor \( 1 \, u = 931.5 \, \text{MeV}/c^2 \), we can convert the mass defect to binding energy \( E_b \):

\[ E_b = \Delta m \cdot 931.5 \, \text{MeV}/c^2 \]

Substituting the value of \( \Delta m \):

\[ E_b = 0.11243 \, u \cdot 931.5 \, \text{MeV}/c^2 \]

Calculating this:

\[ E_b = 104.72 \, \text{MeV} \]

### Final Answer
The binding energy of the nitrogen nucleus is \( \boxed{104.72 \, \text{MeV}} \).