Calculate the binding energy per nucleon for two deuterons combining to form an alpha particle.

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).

$$M_{\text{reactants}} = 2 \times M(^2_1\text{H})$$ $$M_{\text{reactants}} = 2 \times 2.013554 \text{ u} = 4.027108 \text{ u}$$

Step 2: Calculate the mass defect ($\Delta m$).
The mass defect is the difference between the mass of the reactants and the mass of the product ($^4_2\text{He}$).

$$$$