Calculate the mass defect of alpha particle in `MeV//c^(2)` if mass of a-particle is 4.0039 amu.

Answer

To calculate the mass defect of an alpha particle in MeV/c², we will follow these steps:

### Step 1: Determine the mass of the alpha particle
The mass of the alpha particle is given as:
\[ \text{Mass of } \alpha \text{-particle} = 4.0039 \, \text{amu} \]

### Step 2: Calculate the mass of the constituents of the alpha particle
An alpha particle consists of 2 protons and 2 neutrons. The masses of the proton and neutron are given as:
- Mass of a proton \( m_p = 1.00758 \, \text{amu} \)
- Mass of a neutron \( m_n = 1.00897 \, \text{amu} \)

The total mass of the constituents (2 protons and 2 neutrons) can be calculated as follows:
\[ \text{Total mass} = 2 \times m_p + 2 \times m_n \]
\[ = 2 \times 1.00758 + 2 \times 1.00897 \]
\[ = 2.01516 + 2.01794 = 4.0331 \, \text{amu} \]

### Step 3: Calculate the mass defect
The mass defect \( \Delta m \) is the difference between the total mass of the constituents and the actual mass of the alpha particle:
\[ \Delta m = \text{Total mass} - \text{Mass of } \alpha \text{-particle} \]
\[ = 4.0331 \, \text{amu} - 4.0039 \, \text{amu} \]
\[ = 0.0292 \, \text{amu} \]

### Step 4: Convert the mass defect to MeV/c²
To convert the mass defect from atomic mass units to MeV/c², we use the conversion factor:
\[ 1 \, \text{amu} = 931.5 \, \text{MeV/c}^2 \]
Thus, we can calculate:
\[ \Delta m \text{ in MeV/c}^2 = 0.0292 \, \text{amu} \times 931.5 \, \text{MeV/c}^2/\text{amu} \]
\[ = 27.1998 \, \text{MeV/c}^2 \]

### Final Answer
The mass defect of the alpha particle is approximately:
\[ \Delta m \approx 27.2 \, \text{MeV/c}^2 \]

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