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An alpha nucleus of energy 1/2 mv² bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to
- 1/Ze
- v²
- 1/m
- 1/v⁴
Correct answer: 1/v⁴
Solution
The distance of closest approach is determined by equating the initial kinetic energy of the alpha particle to the electrostatic potential energy at the closest distance. This gives the distance proportional to 1/v⁴, as the kinetic energy is proportional to v² and the potential energy is inversely proportional to the distance.
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