To find the energy released in this nuclear reaction, we use the concept of mass defect and Einstein's mass-energy equivalence principle. The mass defect is the difference between the mass of the reactants and the mass of the products in a nuclear reaction. According to Einstein's relation, $$E=mc^2$$, where $$E$$ is the energy released, $$m$$ is the mass defect, and $$c$$ is the speed of light in vacuum.

Given data:

Mass of deuteron = $$2.01355\, \mathrm{amu}$$
Mass of helium nucleus = $$4.0028\, \mathrm{amu}$$

The reaction involves two deuteron nuclei combining into one helium nucleus. First, let's calculate the total mass of the reactants (2 deuterons):

$$\text{Total mass of reactants} = 2 \times \text{mass of deuteron} = 2 \times 2.01355\, \mathrm{amu}$$

$$\text{Total mass of reactants} = 4.0271\, \mathrm{amu}$$

Now, let's find the mass defect ($$\Delta m$$), which is the difference between the mass of the reactants and the mass of the product (helium nucleus):

$$\Delta m = \text{Total mass of reactants} - \text{mass of product}$$

$$\Delta m = 4.0271\, \mathrm{amu} - 4.0028\, \mathrm{amu}$$

$$\Delta m = 0.0243\, \mathrm{amu}$$

To convert the mass defect from atomic mass units (amu) to kilograms (kg), we use the conversion factor $$1\, \mathrm{amu} = 1.660539040 \times 10^{-27}\, \mathrm{kg}$$:

$$\Delta m \,(\mathrm{kg}) = 0.0243\, \mathrm{amu} \times 1.660539040 \times 10^{-27} \, \mathrm{kg/amu}$$

$$\Delta m \, (\mathrm{kg}) = 4.03311 \times 10^{-29}\, \mathrm{kg}$$

The energy released can now be calculated using the formula $$E=mc^2$$, where $$c = 2.99792458 \times 10^8 \, \mathrm{m/s}$$ (speed of light):

$$E = (4.03311 \times 10^{-29}\, \mathrm{kg}) \times (2.99792458 \times 10^8 \, \mathrm{m/s})^2$$

$$E = 3.62894 \times 10^{-12}\, \mathrm{J}$$

To convert energy from Joules to Mega-electronvolts ($$\mathrm{MeV}$$), we use $$1\, \mathrm{J} = 6.242 \times 10^{12}\, \mathrm{MeV}$$:

$$E = 3.62894 \times 10^{-12}\, \mathrm{J} \times 6.242 \times 10^{12}\, \mathrm{MeV/J}$$

$$E = 22.65\, \mathrm{MeV}$$

The energy released is approximately $$22.65\, \mathrm{MeV}$$, which is closest to Option C, $$22.62\, \mathrm{MeV}$$. Therefore, Option C is the correct answer.

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