The nuclear binding energy for Ar (39.962384 amu) is : (given mass of proton and neuron are 1.007825 amu and 1.008665amu respectively)

Options

A. 343.62 MeV
B. 0.369096 MeV
C. 931 MeV
D. None of these

Explanation

To calculate the nuclear binding energy for Argon (Ar), we will follow these steps:

### Step 1: Determine the number of protons and neutrons in Argon-40
Argon-40 has an atomic number of 18, which means it has 18 protons. The mass number is 40, so the number of neutrons can be calculated as:
\[ \text{Number of Neutrons} = \text{Mass Number} - \text{Number of Protons} = 40 - 18 = 22 \]

### Step 2: Calculate the total mass of protons and neutrons
Using the given masses:
- Mass of one proton = 1.007825 amu
- Mass of one neutron = 1.008665 amu

The total mass of protons is:
\[ \text{Total Mass of Protons} = 18 \times 1.007825 \, \text{amu} = 18.14085 \, \text{amu} \]

The total mass of neutrons is:
\[ \text{Total Mass of Neutrons} = 22 \times 1.008665 \, \text{amu} = 22.19163 \, \text{amu} \]

### Step 3: Calculate the combined mass of protons and neutrons
Now, we can find the combined mass of protons and neutrons:
\[ \text{Combined Mass} = \text{Total Mass of Protons} + \text{Total Mass of Neutrons} \]
\[ \text{Combined Mass} = 18.14085 \, \text{amu} + 22.19163 \, \text{amu} = 40.33248 \, \text{amu} \]

### Step 4: Calculate the mass defect
The mass defect (\( \Delta m \)) is the difference between the combined mass of protons and neutrons and the actual mass of the Argon nucleus:
\[ \Delta m = \text{Combined Mass} - \text{Actual Mass of Argon} \]
\[ \Delta m = 40.33248 \, \text{amu} - 39.962384 \, \text{amu} = 0.370096 \, \text{amu} \]

### Step 5: Calculate the binding energy
The binding energy (BE) can be calculated using the mass defect and the conversion factor (1 amu = 931.5 MeV):
\[ \text{Binding Energy} = \Delta m \times 931.5 \, \text{MeV/amu} \]
\[ \text{Binding Energy} = 0.370096 \, \text{amu} \times 931.5 \, \text{MeV/amu} \]
\[ \text{Binding Energy} \approx 344.3 \, \text{MeV} \]

### Final Result
The nuclear binding energy for Argon-40 is approximately **344.3 MeV**.

---