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Question #43709

Difficulty: 8/10 | 🟢 Free

The Question

A stationary nucleus undergoes nuclear fission, releasing a total kinetic energy $Q$ and splitting into two fragments of masses $m$ and $2m$ . The lighter fragment, carrying a charge $q$ , is directed towards a massive, stationary target nucleus of charge $Q_t$ . Assume the target nucleus is infinitely massive and fixed in space. If the impact parameter of the lighter fragment is $b = \frac{3\sqrt{2} q Q_t}{8 \pi \epsilon_0 Q}$ , what is the distance of closest approach between the lighter fragment and the target nucleus?

Options

A.
$\frac{3 q Q_t}{4 \pi \epsilon_0 Q}$
B.
$\frac{3 q Q_t}{8 \pi \epsilon_0 Q}$
C.
$\frac{3\sqrt{2} q Q_t}{8 \pi \epsilon_0 Q}$
D.
$\frac{3\sqrt{3} q Q_t}{8 \pi \epsilon_0 Q}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Nuclear Fission Energy Balance|Impact Parameter Geometry|Coulombic Central Force

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to couple nuclear energy kinematics with orbital mechanics in a Coulomb field.

The primary trap lies in the geometry of the distance of closest approach.

Students frequently misapply energy conservation by assuming the kinetic energy at $r_{min}$ is zero (treating it as a 1D head-on collision), which leads to the incorrect answer $r_{min} = d_0$ .

Another common error is failing to correctly partition the fission $Q$ -value using momentum conservation, incorrectly assigning the full energy $Q$ to the lighter fragment.

The problem rigorously demands the simultaneous application of angular momentum and energy conservation to account for the centrifugal barrier in a non-head-on trajectory.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Nuclei - Class 12
Concept	Nuclear Fission Energy Balance
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free