The mass of proton,neutron and helium nucleus are respectively `1.0073u,1.0087u` and `4.0015u`.The binding energy of helium nucleus is :

Options

A. `14.2MeV`
B. `7.1MeV`
C. `56.8MeV`
D. `28.4MeV`

Answer

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

### Step 1: Identify the given masses
- Mass of proton (m_p) = 1.0073 u
- Mass of neutron (m_n) = 1.0087 u
- Mass of helium nucleus (m_He) = 4.0015 u

### Step 2: Calculate the mass defect (ΔM)
The mass defect is calculated using the formula:
\[ \Delta M = (2 \times m_p + 2 \times m_n) - m_{He} \]

Substituting the values:
\[ \Delta M = (2 \times 1.0073 + 2 \times 1.0087) - 4.0015 \]

Calculating the values:
\[ \Delta M = (2.0146 + 2.0174) - 4.0015 \]
\[ \Delta M = 4.032 - 4.0015 \]
\[ \Delta M = 0.0305 \, u \]

### Step 3: Convert the mass defect to energy (binding energy)
The binding energy (BE) can be calculated using the formula:
\[ BE = \Delta M \times 931.5 \, \text{MeV/u} \]

Substituting the value of ΔM:
\[ BE = 0.0305 \times 931.5 \, \text{MeV} \]

Calculating the binding energy:
\[ BE = 28.41075 \, \text{MeV} \]

### Step 4: Round off the result
The binding energy can be rounded to:
\[ BE \approx 28.41 \, \text{MeV} \]

### Final Answer
The binding energy of the helium nucleus is approximately **28.41 MeV**.

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