Calculate the binding energy of a deutron. Given that
mass of proton = 1.007825 amu
mass of neutron = 1.008665 amu
mass of deutron = 2.014103 amu

Answer

To calculate the binding energy of a deuteron, we will follow these steps:

### Step 1: Identify the masses involved
- Mass of proton (m_p) = 1.007825 amu
- Mass of neutron (m_n) = 1.008665 amu
- Mass of deuteron (m_d) = 2.014103 amu

### Step 2: Calculate the total mass of the individual nucleons
The total mass of the individual nucleons (1 proton and 1 neutron) can be calculated as:
\[ \text{Total mass of nucleons} = m_p + m_n \]
Substituting the values:
\[ \text{Total mass of nucleons} = 1.007825 \, \text{amu} + 1.008665 \, \text{amu} = 2.016490 \, \text{amu} \]

### Step 3: Calculate the mass defect (Δm)
The mass defect is the difference between the total mass of the individual nucleons and the actual mass of the deuteron:
\[ \Delta m = \text{Total mass of nucleons} - m_d \]
Substituting the values:
\[ \Delta m = 2.016490 \, \text{amu} - 2.014103 \, \text{amu} = 0.002387 \, \text{amu} \]

### Step 4: Convert the mass defect to energy (binding energy)
The binding energy (BE) can be calculated using the formula:
\[ BE = \Delta m \times c^2 \]
Where \(c^2\) is approximately 931.5 MeV/amu. Thus:
\[ BE = 0.002387 \, \text{amu} \times 931.5 \, \text{MeV/amu} \]
Calculating this gives:
\[ BE \approx 2.224 \, \text{MeV} \]

### Step 5: Final result
The binding energy of the deuteron is approximately:
\[ BE \approx 2.22 \, \text{MeV} \]

### Summary
The binding energy of a deuteron is approximately 2.22 MeV.

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