The mass of helium atom is 4.0026 amu, while that of the neutron and proton are 1.0087 and 1.0078 amu respectively on the same scale. Hence, the nuclear binding energy per nucleon in the helium atom is about

Options

A. 5 MeV
B. 12 MeV
C. 14 MeV
D. 7 MeV

Explanation

To find the nuclear binding energy per nucleon in a helium atom, we will follow these steps:

### Step 1: Determine the Mass of the Helium Nucleus
The helium nucleus consists of:
- 2 protons
- 2 neutrons

Given:
- Mass of a proton = 1.0078 amu
- Mass of a neutron = 1.0087 amu
- Mass of helium atom = 4.0026 amu

### Step 2: Calculate the Total Mass of Protons and Neutrons
Calculate the total mass of the nucleons (protons and neutrons) in the helium nucleus:
- Total mass of protons = 2 × 1.0078 amu = 2.0156 amu
- Total mass of neutrons = 2 × 1.0087 amu = 2.0174 amu

Now, add these two masses together:
- Total mass of nucleons = Total mass of protons + Total mass of neutrons
- Total mass of nucleons = 2.0156 amu + 2.0174 amu = 4.0330 amu

### Step 3: Calculate the Mass Defect
The mass defect (Δm) is the difference between the total mass of the nucleons and the actual mass of the helium atom:
- Δm = Total mass of nucleons - Mass of helium atom
- Δm = 4.0330 amu - 4.0026 amu = 0.0304 amu

### Step 4: Calculate the Binding Energy
The binding energy (BE) can be calculated using the mass defect and Einstein's equation, where 1 amu corresponds to approximately 931 MeV:
- Binding Energy (BE) = Δm × 931 MeV
- BE = 0.0304 amu × 931 MeV/amu = 28.3 MeV (approximately)

### Step 5: Calculate the Binding Energy per Nucleon
Since there are 4 nucleons in a helium nucleus, we can find the binding energy per nucleon:
- Binding Energy per Nucleon = Total Binding Energy / Number of Nucleons
- Binding Energy per Nucleon = 28.3 MeV / 4 = 7.075 MeV (approximately)

### Conclusion
The nuclear binding energy per nucleon in the helium atom is approximately **7 MeV**.

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