Question

The energy is emitted when two nuclei of masses m\(_1\) and m\(_2\) are fused together to make a nucleus of mass m. In this process :

• A. (m\(_1\) + m\(_2\)) \(<\) m
• B. (m\(_1\) + m\(_2\)) \(>\) m
• C. (m\(_1\) + m\(_2\)) = m
• D. m\(_1\)m\(_2\) \(>\) m\(^2\)

Hint:

In any exothermic nuclear reaction (one that releases energy), whether fusion or fission, the total mass of the products is always less than the total mass of the reactants. This "missing" mass is converted into the released energy.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question relates to the concept of mass-energy equivalence in nuclear reactions, specifically nuclear fusion. In fusion, energy is released because the binding energy per nucleon of the product nucleus is greater than that of the reactant nuclei.
Step 2: Key Formula or Approach:
The process is governed by Einstein's mass-energy equivalence principle, \(E = mc^2\).
For energy to be emitted (released), there must be a decrease in the total mass of the system. This loss of mass, called the mass defect (\(\Delta m\)), is converted into energy.
Step 3: Detailed Explanation:
The initial total mass of the system is the sum of the masses of the two nuclei, \(m_{initial} = m_1 + m_2\).
The final mass of the system is the mass of the new nucleus, \(m_{final} = m\).
Energy is emitted in the process. This means the final state has less energy than the initial state, which corresponds to a decrease in mass.
Therefore, the initial mass must be greater than the final mass. \[ m_{initial}>m_{final} \] \[ m_1 + m_2>m \] The energy released is calculated as \(E = (m_1 + m_2 - m)c^2\).
Step 4: Final Answer:
For energy to be emitted during fusion, the sum of the initial masses must be greater than the final mass. Thus, \( (m_1 + m_2)>m \).