Question

If binding energy per nucleon of deuteron and \( \alpha \)-particle are 1.25 MeV and 7.4 MeV respectively, then find the value of \( Q \) in the following reaction: 

\[2  ^1_1H \rightarrow 2  ^4_2He + Q\]

Hint:

The \( Q \)-value represents the net energy released in a nuclear reaction and depends on the difference in binding energies.

Answer 1

Step 1: Binding Energy and \( Q \)-Value.
The \( Q \)-value of a nuclear reaction is given by the difference in the total binding energy of the products and the reactants. The formula is: \[ Q = \left( \text{Total Binding Energy of Products} \right) - \left( \text{Total Binding Energy of Reactants} \right) \]
Step 2: Calculating the Binding Energies.
The binding energy per nucleon of deuteron is 1.25 MeV, and for the \( \alpha \)-particle, it is 7.4 MeV. The binding energy of the reactants (deuterons) is \( 2 \times 1.25 \) MeV. The binding energy of the products (two \( \alpha \)-particles) is \( 2 \times 7.4 \) MeV. \[ Q = 2 \times 7.4 - 2 \times 1.25 = 14.8 - 2.5 = 12.3 \, \text{MeV} \]
Step 3: Conclusion.
The value of \( Q \) is \( 12.3 \, \text{MeV} \).