Question

The nuclear reaction \(_1\mathrm{H}^1 + _1\mathrm{H}^1 \rightarrow _2\mathrm{He}^4\) (mass of deuteron = 2.0141 amu and of He = 4.0024 amu) is

• A. fusion reaction releasing 24 MeV energy
• B. fusion reaction absorbing 24 MeV energy
• C. fission reaction releasing 0.0258 MeV energy
• D. fission reaction absorbing 0.0258 MeV energy

Hint:

1 amu = 931.5 MeV/\(c^2\).

Answer 1

The Correct Option is A

The given question involves a nuclear reaction: \(_1\mathrm{H}^1 + _1\mathrm{H}^1 \rightarrow _2\mathrm{He}^4\). This is a classic example of a fusion reaction. In a fusion reaction, lighter nuclei combine to form a heavier nucleus, releasing energy in the process. Let's analyze the details of this reaction to confirm the correct answer.

1. Identify the given nuclei and their masses:
   • Deuteron (heavy hydrogen, \(_1\mathrm{H}^1\)) has a mass of 2.0141 atomic mass units (amu).
   • Helium (\(_2\mathrm{He}^4\)) has a mass of 4.0024 amu.
2. Calculate the mass defect:

The mass defect is the difference in mass before and after the reaction.

1. \(\text{Mass defect} = \left(2 \times 2.0141 \, \text{amu}\right) - 4.0024 \, \text{amu}\)

Calculating the masses:

1. \(\text{Mass of reactants} = 2 \times 2.0141 = 4.0282 \, \text{amu}\) \(\text{Mass defect} = 4.0282 \, \text{amu} - 4.0024 \, \text{amu} = 0.0258 \, \text{amu}\)
2. Convert the mass defect into energy:

Using Einstein's mass-energy equivalence formula, \(E = mc^2\), where \(c\) is the speed of light (approximately \(3 \times 10^8 \, \text{m/s}\)), we can convert the mass defect into energy.

In nuclear physics, it is convenient to use the conversion: 1 amu = 931 MeV. Therefore,

1. \(E = 0.0258 \, \text{amu} \times 931 \, \text{MeV/amu}\) \(E = 24.0158 \, \text{MeV}\)
2. Conclusion:

The reaction releases approximately 24 MeV of energy. This supports the correct answer: fusion reaction releasing 24 MeV energy.