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 components of the nitrogen nucleus
The nitrogen nucleus consists of:
- 7 protons
- 7 neutrons

### Step 2: Calculate the total mass of the protons and neutrons
Using the given data:
- Mass of a hydrogen atom (which is approximately the mass of a proton) = \( 1.00783 \, u \)
- Mass of a neutron = \( 1.00867 \, u \)

The total mass of the protons:
\[ \text{Total mass of protons} = 7 \times 1.00783 \, u = 7.05481 \, u \]

The total mass of the neutrons:
\[ \text{Total mass of neutrons} = 7 \times 1.00867 \, u = 7.06069 \, u \]

### Step 3: Calculate the combined mass of protons and neutrons
\[ \text{Total mass} = \text{Total mass of protons} + \text{Total mass of neutrons} = 7.05481 \, u + 7.06069 \, u = 14.1155 \, u \]

### Step 4: Calculate the mass defect
The mass defect \( \Delta m \) is given by:
\[ \Delta m = \text{Total mass of nucleons} - \text{Mass of nitrogen nucleus} \]
Given the mass of the nitrogen nucleus \( _7N^{14} = 14.00307 \, u \):
\[ \Delta m = 14.1155 \, u - 14.00307 \, u = 0.11243 \, u \]

### Step 5: Calculate the binding energy
The binding energy \( BE \) can be calculated using the formula:
\[ BE = \Delta m \times 931 \, \text{MeV} \]
Substituting the value of \( \Delta m \):
\[ BE = 0.11243 \, u \times 931 \, \text{MeV/u} = 104.67 \, \text{MeV} \]

### Final Answer
The calculated value of the binding energy of the nucleus of the nitrogen atom \( _7N^{14} \) is approximately **104.67 MeV**.

---