Using the following data .Mass hydrogen atom = 1.00783 u Mass of neutron = 1.00867 u Mass of nitrogen atom `(._7N^(14))` 14.00307 u The calculated value of the binding energy of the nucleus of the nitrogen atom `(._7 N^(14))` is close to

Options

A. 56 MeV
B. 98 MeV
C. 104 MeV
D. 112 MeV

Answer

To calculate the binding energy of the nitrogen nucleus \( _7N^{14} \), we will follow these steps:

### Step 1: Identify the number of protons and neutrons in the nitrogen nucleus
The nitrogen nucleus \( _7N^{14} \) has:
- Number of protons (Z) = 7
- Number of neutrons (N) = 14 - 7 = 7

### Step 2: Calculate the total mass of the nucleons
The total mass of the nucleons can be calculated using the formula:
\[ \text{Total mass of nucleons} = (Z \times \text{mass of proton}) + (N \times \text{mass of neutron}) \]
Substituting the values:
- Mass of proton = 1.00783 u
- Mass of neutron = 1.00867 u

Calculating the total mass:
\[ \text{Total mass of nucleons} = (7 \times 1.00783) + (7 \times 1.00867) \]
\[ = 7.05481 + 7.06069 = 14.1155 \text{ u} \]

### Step 3: Calculate the mass defect
The mass defect is given by:
\[ \text{Mass defect} = \text{Total mass of nucleons} - \text{mass of nucleus} \]
Given:
- Mass of nitrogen nucleus = 14.00307 u

Calculating the mass defect:
\[ \text{Mass defect} = 14.1155 - 14.00307 = 0.11243 \text{ u} \]

### Step 4: Convert mass defect to binding energy
The binding energy (BE) can be calculated using the formula:
\[ \text{Binding Energy} = \text{Mass defect} \times 931 \text{ MeV/u} \]
Substituting the mass defect:
\[ \text{Binding Energy} = 0.11243 \times 931 \approx 104.104 \text{ MeV} \]

### Final Answer
The binding energy of the nucleus of the nitrogen atom \( _7N^{14} \) is approximately **104 MeV**.