The mass of proton is 1.0073 u and that of neutron is 1.0087 u ( u=atomic mass unit ). The binding energy of `._2^4He` , if mass of `._2^4He ` is 4.0015 u is

Options

A. 0.0305 erg
B. 0.0305 J
C. 28.4 MeV
D. 0.061 u

Explanation

To find the binding energy of the helium-4 nucleus, we will follow these steps:

### Step 1: Identify the components of the helium-4 nucleus
Helium-4 (\(^4_2He\)) consists of:
- 2 protons
- 2 neutrons

### Step 2: Calculate the total mass of the individual nucleons
Using the given masses:
- Mass of one proton = 1.0073 u
- Mass of one neutron = 1.0087 u

The total mass of the nucleons (2 protons + 2 neutrons) is calculated as follows:
\[ \text{Total mass of nucleons} = (2 \times \text{mass of proton}) + (2 \times \text{mass of neutron}) \]
\[ = (2 \times 1.0073 \, \text{u}) + (2 \times 1.0087 \, \text{u}) \]
\[ = 2.0146 \, \text{u} + 2.0174 \, \text{u} = 4.0320 \, \text{u} \]

### Step 3: Calculate the mass defect
The mass defect (\(\Delta m\)) is the difference between the total mass of the nucleons and the actual mass of the helium-4 nucleus:
\[ \Delta m = \text{Total mass of nucleons} - \text{mass of helium-4 nucleus} \]
\[ = 4.0320 \, \text{u} - 4.0015 \, \text{u} = 0.0305 \, \text{u} \]

### Step 4: Convert mass defect to binding energy
The binding energy (BE) can be calculated using the formula:
\[ \text{Binding Energy} = \Delta m \times 931 \, \text{MeV/u} \]
Substituting the mass defect:
\[ \text{Binding Energy} = 0.0305 \, \text{u} \times 931 \, \text{MeV/u} \approx 28.4 \, \text{MeV} \]

### Final Answer
The binding energy of \(^4_2He\) is approximately **28.4 MeV**.

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