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Question #43638

Difficulty: 8/10 | 🟢 Free

The Question

An alpha particle of mass $m$ and charge $+2e$ is fired with an initial speed $v_0$ directly towards a free, initially stationary Oxygen nucleus ( $^{16}_{8}\text{O}$ ) of mass $4m$ and charge $+8e$ . Assume the system is isolated and no other forces act on the particles. What is the distance of closest approach between the alpha particle and the Oxygen nucleus? (Here $\epsilon_0$ is the vacuum permittivity).

Options

A.
$\frac{10 e^2}{\pi \epsilon_0 m v_0^2}$
B.
$\frac{8 e^2}{\pi \epsilon_0 m v_0^2}$
C.
$\frac{5 e^2}{\pi \epsilon_0 m v_0^2}$
D.
$\frac{2 e^2}{\pi \epsilon_0 m v_0^2}$

Check Your Answer

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

Distance of Closest Approach|Reduced Mass Effect|Variable Force Integration

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to correctly apply the conservation of energy in a two-body scattering problem where the target is not fixed.

A common trap is to assume the target nucleus remains stationary, erroneously equating the entire initial kinetic energy of the alpha particle to the electrostatic potential energy.

This neglects the recoil of the target nucleus and the residual kinetic energy of the center of mass.

By shifting to the Center of Mass frame and utilizing the reduced mass concept, students must recognize that only the relative kinetic energy is available to overcome the variable Coulomb repulsion.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Atoms - Class 12
Concept	Distance of Closest Approach
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free