The masses of neutron and proton are `1.0087` a.m.u. and `1.0073` a.m.u. respectively. If the neutrons and protons combine to form a helium nucleus (alpha particle) of mass `4.0015`a.m.u. The binding energy of the helium nucleus will be `(1 a.m.u. = 931 MeV)`.

Options

A. 28.4meV
B. 20.8 MeV
C. 27.3 MeV
D. 14.2 MeV

Explanation

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

### Step 1: Identify the number of protons and neutrons in helium
A helium nucleus consists of 2 protons and 2 neutrons.

### Step 2: Calculate the total mass of the individual nucleons
The total mass of the individual nucleons (protons and neutrons) can be calculated as follows:

- Mass of 2 protons = \(2 \times 1.0073 \, \text{a.m.u.} = 2.0146 \, \text{a.m.u.}\)
- Mass of 2 neutrons = \(2 \times 1.0087 \, \text{a.m.u.} = 2.0174 \, \text{a.m.u.}\)

Now, adding these together gives us the total mass of the nucleons:

\[ \text{Total mass of nucleons} = 2.0146 \, \text{a.m.u.} + 2.0174 \, \text{a.m.u.} = 4.0320 \, \text{a.m.u.} \]

### Step 3: 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:

\[ \Delta m = \text{Total mass of nucleons} - \text{Mass of helium nucleus} \]
\[ \Delta m = 4.0320 \, \text{a.m.u.} - 4.0015 \, \text{a.m.u.} = 0.0305 \, \text{a.m.u.} \]

### Step 4: Convert mass defect to energy (binding energy)
To find the binding energy, we use the conversion factor \(1 \, \text{a.m.u.} = 931 \, \text{MeV}\):

\[ \text{Binding Energy} = \Delta m \times 931 \, \text{MeV} \]
\[ \text{Binding Energy} = 0.0305 \, \text{a.m.u.} \times 931 \, \text{MeV/a.m.u.} = 28.4 \, \text{MeV} \]

### Final Answer
The binding energy of the helium nucleus is \(28.4 \, \text{MeV}\).

---