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If in a nuclear fusion process the masse...

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

A

`m_3=|m_1-m_2|`

B

`m_3 lt (m_1+m_2)`

C

`m_3 gt (m_1+m_2)`

D

`m_3 = m_1 + m_2`

Text Solution

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The correct Answer is:
To solve the problem, we need to analyze the relationship between the masses of the fusing nuclei and the mass of the resultant nucleus in a nuclear fusion process. ### Step-by-Step Solution: 1. **Understanding Nuclear Fusion**: In a nuclear fusion process, two lighter nuclei (with masses \( m_1 \) and \( m_2 \)) combine to form a heavier nucleus (with mass \( m_3 \)). 2. **Mass Defect Concept**: During fusion, some mass is converted into energy, which is known as the mass defect. The mass defect (\( \Delta m \)) can be defined as: \[ \Delta m = (m_1 + m_2) - m_3 \] This means that the total mass of the original nuclei (\( m_1 + m_2 \)) is greater than the mass of the resultant nucleus (\( m_3 \)). 3. **Implication of Mass Defect**: The mass defect is associated with the binding energy of the resultant nucleus. The energy released during the fusion process is due to this mass defect. The binding energy (\( E \)) is given by Einstein's equation: \[ E = \Delta m c^2 \] where \( c \) is the speed of light. 4. **Conclusion**: Since the mass defect is positive, we can conclude that: \[ m_1 + m_2 > m_3 \] This indicates that the mass of the resultant nucleus is less than the sum of the masses of the fusing nuclei. 5. **Final Answer**: Therefore, the correct statement is: \[ m_3 < m_1 + m_2 \]
To solve the problem, we need to analyze the relationship between the masses of the fusing nuclei and the mass of the resultant nucleus in a nuclear fusion process. ### Step-by-Step Solution: 1. **Understanding Nuclear Fusion**: In a nuclear fusion process, two lighter nuclei (with masses \( m_1 \) and \( m_2 \)) combine to form a heavier nucleus (with mass \( m_3 \)). 2. **Mass Defect Concept**: During fusion, some mass is converted into energy, which is known as the mass defect. The mass defect (\( \Delta m \)) can be defined as: \[ ...
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