If in a nuclear fusion process the masses of the fusing nuclei be `m_(1)` and `m_(2)` and the mass of the resuktant nucleus be `m_(3)`, then

Options

A. `m_(3)=m_(1)+m_(2)`
B. `m_(3)=|m_(1)-m_(2)|`
C. `m_(3) lt (m_(1)+m_(2))`
D. `m_(3) gt (m_(1)+m_(2))`

Answer

To solve the problem regarding the nuclear fusion process involving the masses of fusing nuclei \( m_1 \) and \( m_2 \) and the mass of the resultant nucleus \( m_3 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Fusion Process**: In a nuclear fusion reaction, two lighter nuclei (with masses \( m_1 \) and \( m_2 \)) combine to form a heavier nucleus (with mass \( m_3 \)). During this process, some mass is converted into energy according to Einstein's mass-energy equivalence principle.

2. **Apply the Mass-Energy Conservation Principle**: The total mass before the fusion must equal the total mass after the fusion plus the mass equivalent of the energy released. This can be expressed with the equation:
\[ m_1 + m_2 = m_3 + \Delta m \]
where \( \Delta m \) represents the mass converted into energy.

3. **Relate Mass to Energy**: According to Einstein’s equation \( E = \Delta m c^2 \), the energy released during the fusion process can be expressed as:
\[ \Delta m = \frac{E}{c^2} \]
where \( E \) is the energy released and \( c \) is the speed of light.

4. **Rearranging the Equation**: From the conservation of mass-energy, we can rearrange the equation to find the relationship between the masses:
\[ m_3 = m_1 + m_2 - \Delta m \]

5. **Conclude the Mass Relationship**: Since \( \Delta m \) is a positive quantity (as energy is released), we can conclude that:
\[ m_3 < m_1 + m_2 \]
This indicates that the mass of the resultant nucleus \( m_3 \) is less than the sum of the masses of the fusing nuclei \( m_1 \) and \( m_2 \).

6. **Final Result**: Therefore, we can summarize the relationship as:
\[ m_3 < m_1 + m_2 \]
or equivalently,
\[ m_3 < m_1 \quad \text{and} \quad m_3 < m_2 \]