The binding energy per nucleon of `""_(7)N^(14)` nucleus is:
(Mass of `""_(7)N^(14) = 14.00307 u`)
mass of proton = 1.007825 u
mass of neutron = 1.008665 u

Options

A. 7.471 MeV
B. 8.471 MeV
C. `11.9 xx 10^(-13)` J
D. `12.9 xx 10^(-9)` J

Explanation

To find the binding energy per nucleon of the Nitrogen-14 nucleus, we will follow these steps:

### Step 1: Identify the given values
- Mass of Nitrogen-14 nucleus, \( M_N = 14.00307 \, u \)
- Mass of proton, \( M_p = 1.007825 \, u \)
- Mass of neutron, \( M_n = 1.008665 \, u \)
- Atomic number of Nitrogen, \( Z = 7 \)
- Mass number of Nitrogen, \( A = 14 \)

### Step 2: Calculate the number of neutrons
The number of neutrons \( N \) in the nucleus can be calculated using the formula:
\[ N = A - Z \]
Substituting the values:
\[ N = 14 - 7 = 7 \]

### Step 3: Calculate the total mass of protons and neutrons
The total mass of protons and neutrons in the nucleus is given by:
\[ \text{Total mass} = Z \cdot M_p + N \cdot M_n \]
Substituting the values:
\[ \text{Total mass} = 7 \cdot 1.007825 + 7 \cdot 1.008665 \]
Calculating this:
\[ \text{Total mass} = 7.054775 + 7.060655 = 14.11543 \, u \]

### Step 4: Calculate the mass defect \( \Delta M \)
The mass defect \( \Delta M \) is given by:
\[ \Delta M = \text{Total mass} - M_N \]
Substituting the values:
\[ \Delta M = 14.11543 - 14.00307 = 0.11236 \, u \]

### Step 5: Calculate the binding energy \( B.E. \)
The binding energy can be calculated using the formula:
\[ B.E. = \Delta M \cdot c^2 \]
Where \( c^2 \) in terms of energy is \( 931.5 \, \text{MeV/u} \). Thus:
\[ B.E. = 0.11236 \cdot 931.5 \, \text{MeV} \]
Calculating this:
\[ B.E. = 104.663 \, \text{MeV} \]

### Step 6: Calculate the binding energy per nucleon
The binding energy per nucleon is given by:
\[ \text{Binding energy per nucleon} = \frac{B.E.}{A} \]
Substituting the values:
\[ \text{Binding energy per nucleon} = \frac{104.663}{14} \]
Calculating this:
\[ \text{Binding energy per nucleon} = 7.475 \, \text{MeV} \]

### Final Result
The binding energy per nucleon of the Nitrogen-14 nucleus is approximately:
\[ \text{Binding energy per nucleon} \approx 7.47 \, \text{MeV} \]

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