AIPMT PRELIMS 2004 Physics Fusion MCQ Question

In nuclear fusion, two light atomic nuclei combine to form a heavier nucleus, releasing energy in the process. The masses involved in this reaction can be analyzed using the principles of mass-energy equivalence and conservation of mass-energy.

Explanation of the Correct Answer (B: $m_1 < (m_1 + m_2)$)

In any fusion process, the masses of the two fusing nuclei, denoted as $m_1$ and $m_2$, are combined to form a new nucleus with mass $m_3$. According to the law of conservation of mass-energy, the total mass after the fusion process (which is the rest mass of the resultant nucleus $m_3$) will generally be less than the sum of the initial masses of the fusing nuclei, $m_1 + m_2$. This is due to the conversion of some mass into energy, which is released during the fusion.

Thus, we can say:

$$m_3 < (m_1 + m_2)$$

From this, we can also infer that:

$$m_1 < (m_1 + m_2) \quad \text{is always true, since } m_2 > 0.$$

Therefore, option B is correct because it highlights a basic property of the masses of the fusing nuclei, which is that any mass $m_1$ will always be less than the total mass of both nuclei combined.

Explanation of Incorrect Options:

Option A: $m_1 = |m_1 - m_2|$

This option suggests that the mass of one nucleus is equal to the absolute difference between the two masses. This is not a general property of nuclei in fusion. There is no requirement or law that states one mass must equal the absolute difference of the two masses. For example, if $m_1 = 5 \, \text{u}$ and $m_2 = 3 \, \text{u}$, then $|m_1 - m_2| = 2 \, \text{u}$, which is not equal to $m_1$.

Option C: $m_3 > (m_1 + m_2)$

This option contradicts the conservation of mass-energy. In a fusion reaction, the resultant mass $m_3$ is always less than $m_1 + m_2$ due to the mass-energy equivalence principle where some mass is converted to energy. Therefore, this statement is false.

Option D: $m_3 = m_1 + m_2$

This option implies that the mass of the resultant nucleus equals the sum of the masses of the fusing nuclei. This is also incorrect because, during the fusion process, some mass is converted to energy (as described by Einstein's equation $E = mc^2$). Thus, we have:

$$m_3 < (m_1 + m_2)$$

Summary

In summary, the correct answer to the question is option B, which states that $m_1 < (m_1 + m_2)$. This reflects the fundamental understanding that, while the two nuclei are fusing, the resultant nucleus will have less mass than the sum of the individual nuclei due to the conversion of mass into energy. The other options (A, C, and D) are incorrect based on the laws of physics governing nuclear fusion.