Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:

the helium nucleus has more kinetic energy than the thorium nucleus

the helium nucleus has less momentum than the thorium nucleus

the helium nucleus has more momentum than the thorium nucleus

the helium nucleus has less kinetic energy than the thorium nucleus

Conservation of Momentum: The uranium nucleus is initially at rest, so the initial momentum is zero. According to the law of conservation of momentum, the final total momentum must also be zero . $\vec{P}_{initial} = 0$ $\vec{P}_{final} = \vec{P}_{Th} + \vec{P}_{He} = 0 \implies \vec{P}_{Th} = -\vec{P}_{He}$ This means the momenta of the thorium nucleus and the helium nucleus (\alpha particle) are equal in magnitude and opposite in direction ( $P_{Th} = P_{He} = P$ ). Thus, options 2 and 3 are incorrect.
Kinetic Energy Relation: Kinetic energy ( $K$ ) is related to momentum ( $P$ ) and mass ( $m$ ) by the equation $K = \frac{P^2}{2m}$ .
Comparison: Since the magnitudes of momentum ( $P$ ) are the same for both particles, the kinetic energy is inversely proportional to the mass ( $K \propto \frac{1}{m}$ ).

The mass of the helium nucleus ( $m_{He} \approx 4$ u) is much less than the mass of the thorium nucleus ( $m_{Th} \approx 234$ u).
Therefore, the lighter helium nucleus acquires significantly more kinetic energy than the heavier thorium nucleus ( $K_{He} > K_{Th}$ ).

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