If the mass defect of `._(5)B^(11)` is 0.081 u, its average binding energy (in MeV) is

Options

A. 8.60 MeV
B. 6.85 MeV
C. 6.60 MeV
D. 5.86 MeV

Answer

To solve the problem of finding the average binding energy of the nucleus of Boron-11 given its mass defect, we can follow these steps:

### Step 1: Understand the given data
We are given:
- Mass defect of Boron-11, \( \Delta m = 0.081 \, u \)
- Binding energy equivalent of 1 atomic mass unit (u), \( E = 931.5 \, \text{MeV} \)

### Step 2: Calculate the total binding energy
The total binding energy (B.E.) can be calculated using the formula:
\[ \text{Total Binding Energy} = \Delta m \times E \]
Substituting the values:
\[ \text{Total Binding Energy} = 0.081 \, u \times 931.5 \, \text{MeV/u} \]
Calculating this gives:
\[ \text{Total Binding Energy} = 75.4455 \, \text{MeV} \approx 75.45 \, \text{MeV} \]

### Step 3: Determine the number of nucleons
For Boron-11, the mass number (A) is 11. This means the total number of nucleons (protons + neutrons) is:
\[ \text{Number of Nucleons} = 11 \]

### Step 4: Calculate the average binding energy per nucleon
The average binding energy per nucleon (A.B.E.) is given by:
\[ \text{Average Binding Energy} = \frac{\text{Total Binding Energy}}{\text{Number of Nucleons}} \]
Substituting the values:
\[ \text{Average Binding Energy} = \frac{75.45 \, \text{MeV}}{11} \]
Calculating this gives:
\[ \text{Average Binding Energy} \approx 6.8636 \, \text{MeV} \approx 6.86 \, \text{MeV} \]

### Final Answer
Thus, the average binding energy of Boron-11 is approximately \( 6.86 \, \text{MeV} \).