This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

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Answer
2 \times M(^2_1H)$$
Here's how to find the binding energy per nucleon for both scenarios:
a) When two deuterons combine to form an alpha particle:
Step 1: Calculate the total mass of the reactants (two deuterons).
Step 2: Calculate the mass defect (). The mass defect is the difference between the mass of the reactants and the mass of the product ().
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Here's how to find the binding energy per nucleon for both scenarios: a) When two deuterons combine to form an alpha particle: Step 1: Calculate the total mass of the reactants (two deuterons).
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.