Find the binding energy of an `alpha`-particle from the following data.
Mass of helium nucleus `=4.001235 am u`
Mass of proton `=1.007277 am u`
Mass of neutron `=1.00866 am u`
(take `1 am u=931.4813 MeV`).

Explanation

To find the binding energy of an alpha particle (helium nucleus), we can follow these steps:

### Step 1: Identify the parameters
- Mass of helium nucleus (alpha particle), \( m_{\text{He}} = 4.001235 \, \text{am u} \)
- Mass of proton, \( m_p = 1.007277 \, \text{am u} \)
- Mass of neutron, \( m_n = 1.00866 \, \text{am u} \)
- Conversion factor, \( 1 \, \text{am u} = 931.4813 \, \text{MeV} \)

### Step 2: Determine the number of protons and neutrons in the alpha particle
An alpha particle consists of:
- Number of protons (Z) = 2
- Number of neutrons (N) = 2 (since A = Z + N, and for helium, A = 4)

### Step 3: Calculate the total mass of the individual nucleons
The total mass of the nucleons (2 protons and 2 neutrons) is calculated as follows:
\[ \text{Total mass} = Z \cdot m_p + N \cdot m_n = 2 \cdot 1.007277 \, \text{am u} + 2 \cdot 1.00866 \, \text{am u} \]
Calculating this gives:
\[ \text{Total mass} = 2.014554 \, \text{am u} + 2.01732 \, \text{am u} = 4.031874 \, \text{am u} \]

### Step 4: Calculate the mass defect
The mass defect (\( \Delta m \)) is the difference between the total mass of the individual nucleons and the actual mass of the helium nucleus:
\[ \Delta m = \text{Total mass} - m_{\text{He}} = 4.031874 \, \text{am u} - 4.001235 \, \text{am u} \]
Calculating this gives:
\[ \Delta m = 0.030639 \, \text{am u} \]

### Step 5: Convert the mass defect to energy (binding energy)
Using the conversion factor, we convert the mass defect to binding energy (\( E_b \)):
\[ E_b = \Delta m \cdot (931.4813 \, \text{MeV/am u}) = 0.030639 \, \text{am u} \cdot 931.4813 \, \text{MeV/am u} \]
Calculating this gives:
\[ E_b = 28.539 \, \text{MeV} \]

### Step 6: Conclusion
The binding energy of the alpha particle is \( 28.539 \, \text{MeV} \).