What will be the energy released in the fusion process of two lighter nuclei of masses \( m_1 \) and \( m_2 \) into a nucleus of mass M?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( [(m_1 + m_2) - M]\,c^{2} \)
By Einstein's mass-energy relation, the energy released in a nuclear reaction is the decrease in mass multiplied by \( c^{2} \). In fusion the final nucleus is lighter than the two nuclei that joined, and the lost mass appears as energy.
\( \Delta m = (m_1 + m_2) - M \)
\( E = \Delta m\,c^{2} = [(m_1 + m_2) - M]\,c^{2} \)
Shortcut: The energy released must be positive, and \( M \lt m_1 + m_2 \) for fusion. Option (2) is the negative of this value, and Options (3) and (4) do not use the total mass of the two nuclei at all, so Option (1) is the only one left.