Question

In a nuclear fusion reaction, two nuclei \(A\) and \(B\) fuse to produce a nucleus \(C\), releasing an amount of energy \(\Delta E\) in the process. If the mass defects of the three nuclei are \(\Delta M_A\), \(\Delta M_B\) and \(\Delta M_C\) respectively, then which of the following relations is true? ( \(c\) is the speed of light)

• A. \( \Delta M_A + \Delta M_B = \Delta M_C + \frac{\Delta E}{c^2} \)
• B. \( \Delta M_A - \Delta M_B = \Delta M_C + \frac{\Delta E}{c^2} \)
• C. \( \Delta M_A - \Delta M_B = \Delta M_C - \frac{\Delta E}{c^2} \)
• D. \( \Delta M_A + \Delta M_B = \Delta M_C - \frac{\Delta E}{c^2} \)

Hint:

In fusion, binding energy increases → mass defect decreases → energy is released according to \(E = mc^2\).

Answer 1

The Correct Option is D

Step 1: Concept of mass defect.
Mass defect represents the difference between the mass of nucleons and the actual mass of the nucleus.

Step 2: Energy released in fusion.
In a fusion reaction, energy is released due to increase in binding energy, which corresponds to a decrease in mass.
\[ \Delta E = \Delta m \, c^2 \]

Step 3: Total mass defect relation.
Initial total mass defect:
\[ \Delta M_A + \Delta M_B \]
Final mass defect:
\[ \Delta M_C \]

Step 4: Relation between energy and mass defect.
Since energy is released, total mass defect decreases:
\[ \Delta M_A + \Delta M_B = \Delta M_C - \frac{\Delta E}{c^2} \]

Step 5: Final conclusion.
\[ \boxed{\Delta M_A + \Delta M_B = \Delta M_C - \frac{\Delta E}{c^2}} \] Hence, correct answer is option (D).