The binding energy per nucleon number for deutron `H_(1)^(2)`and helium ` He_(2)^(4)` are `1.1 MeV` and `7.0 MeV` respectively . The energy released when two deuterons fase to form a belium nucleus `He_(2)^(4)` is ……..

Options

A. `20.8 MeV`
B. `16.6 MeV`
C. `25.2 MeV`
D. `23.6 MeV`

Answer

To find the energy released when two deuterons fuse to form a helium nucleus, we can follow these steps:

### Step 1: Identify the binding energy per nucleon
The binding energy per nucleon for deuteron (H₂) is given as 1.1 MeV, and for helium (He₄) it is 7.0 MeV.

### Step 2: Calculate the binding energy of the reactants (deuterons)
Since each deuteron has 2 nucleons, the total binding energy for two deuterons is calculated as follows:
\[ \text{Binding Energy of Deuterons} = \text{Number of Deuterons} \times \text{Binding Energy per Nucleon} \times \text{Number of Nucleons} \]
\[ \text{Binding Energy of Deuterons} = 2 \times 1.1 \, \text{MeV} \times 2 = 4.4 \, \text{MeV} \]

### Step 3: Calculate the binding energy of the product (helium nucleus)
The binding energy for helium (He₄) can be calculated as:
\[ \text{Binding Energy of Helium} = \text{Binding Energy per Nucleon} \times \text{Number of Nucleons} \]
\[ \text{Binding Energy of Helium} = 7.0 \, \text{MeV} \times 4 = 28.0 \, \text{MeV} \]

### Step 4: Calculate the energy released during the fusion
The energy released during the fusion process can be calculated using the difference in binding energies:
\[ \text{Energy Released} = \text{Binding Energy of Products} - \text{Binding Energy of Reactants} \]
\[ \text{Energy Released} = 28.0 \, \text{MeV} - 4.4 \, \text{MeV} = 23.6 \, \text{MeV} \]

### Final Answer
The energy released when two deuterons fuse to form a helium nucleus is **23.6 MeV**.

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