If the mass of proton= 1.008 a.m.u. and mass of neutron=1.009a.m.u. then binding energy per nucleon for `._(4)Be^9` (mass=9.012 amu) would be-

Options

A. 0.065 MeV
B. 60 .44MeV
C. 0.7 MeV
D. 6.72 MeV

Explanation

To find the binding energy per nucleon for the isotope Beryllium-9 (Be-9), we can follow these steps:

### Step 1: Determine the number of protons and neutrons in Be-9
Beryllium (Be) has an atomic number of 4, which means it has 4 protons. The mass number of Be-9 is 9, so the number of neutrons can be calculated as follows:

\[ \text{Number of neutrons} = \text{Mass number} - \text{Number of protons} = 9 - 4 = 5 \]

### Step 2: Calculate the total mass of the nucleons
The total mass of the nucleons (protons and neutrons) can be calculated using their respective masses:

\[ \text{Total mass} = (\text{Number of protons} \times \text{mass of proton}) + (\text{Number of neutrons} \times \text{mass of neutron}) \]

Substituting the values:

\[ \text{Total mass} = (4 \times 1.008 \, \text{a.m.u.}) + (5 \times 1.009 \, \text{a.m.u.}) \]
\[ = 4.032 \, \text{a.m.u.} + 5.045 \, \text{a.m.u.} = 9.077 \, \text{a.m.u.} \]

### Step 3: Calculate the mass defect
The mass defect is the difference between the total mass of the nucleons and the actual mass of the nucleus:

\[ \text{Mass defect} = \text{Total mass of nucleons} - \text{Actual mass of nucleus} \]
\[ = 9.077 \, \text{a.m.u.} - 9.012 \, \text{a.m.u.} = 0.065 \, \text{a.m.u.} \]

### Step 4: Convert the mass defect to energy
To find the binding energy, we convert the mass defect from atomic mass units to energy using Einstein's equation \(E = mc^2\). The conversion factor is approximately \(931.5 \, \text{MeV/c}^2\) per a.m.u.:

\[ \text{Binding Energy} = \text{Mass defect} \times 931.5 \, \text{MeV} \]
\[ = 0.065 \, \text{a.m.u.} \times 931.5 \, \text{MeV/a.m.u.} \approx 60.6 \, \text{MeV} \]

### Step 5: Calculate the binding energy per nucleon
Finally, we calculate the binding energy per nucleon by dividing the total binding energy by the number of nucleons:

\[ \text{Binding Energy per Nucleon} = \frac{\text{Total Binding Energy}}{\text{Number of nucleons}} = \frac{60.6 \, \text{MeV}}{9} \approx 6.73 \, \text{MeV} \]

### Final Answer
The binding energy per nucleon for Be-9 is approximately **6.73 MeV**.

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