In separate experiments, four different particles each start from far away with the same speed and impinge directly on a gold nucleus.The masses and charges of the particles are Rank the particles according to the distance of closest approach to the gold nucleus, from smallest to largest.

Question

In separate experiments, four different particles each start from far away with the same speed and impinge directly on a gold nucleus.The masses and charges of the particles are  Rank the particles according to the distance of closest approach to the gold nucleus, from smallest to largest.

Quizplus · Accepted Answer

The distance of closest approach is determined by the Coulomb force between the charged particles and the gold nucleus. The force is given by F = kqQ/r^2, where k is Coulomb's constant, q and Q are the charges of the particles and nucleus, respectively, and r is the distance between them.
The key to solving this problem is to note that the Coulomb force depends on the product of the charges, qQ. Particle 1 has the highest charge (+3e) and particle 4 has the lowest charge (-1e), so particle 1 will experience the greatest Coulomb repulsion and particle 4 the least. Hence, particle 1 will have the largest closest approach distance and particle 4 the smallest. 
Next, we need to compare particles 2 and 3. They have the same charge (-2e) but different masses. According to Newton's second law, F = ma, the acceleration of a particle is inversely proportional to its mass. Thus, particle 2 will experience a larger acceleration and hence a larger closest approach distance than particle 3. Hence, the order of closest approach distances is: 4 < 3 < 1 and 2 tie. Therefore, the answer is C.

In Separate Experiments, Four Different Particles Each Start from Far