Can I get the answer for (f) Consider the energy diagram below. (a) Describe the

Question

Can I get the answer for (f)

Consider the energy diagram below. (a) Describe the motion of a particle at position 1 with energy TE1. Which direction will it be moving? (Are you sure?!) How do you know? Which direction will it be accelerating? How do you know? (b) How will a particle with energy TE2 behave differently than a particle with energy TE1? (c) Identify points of stable and unstable equilibrium. (d) For particles of any given energy (TE1-4), can a particle be stationary at any of the equilibrium points? For a particle with energy TE2, describe the force on the particle at points 2, 3, 4, 5, and 6. Specifically, is the force to the left or right, and at which point(s) is the force greatest and least? (e) Where could you possibly find a particle with energy TE3? Identify the turning points for such a particle. Describe the motion of a particle with energy TE3, specifically, how is it different for the two possible regions where it can exist? (f) Explain the existence or lack thereof for a particle with energy TE4 at point 2.

Explanation / Answer

I can safely assume you know the answer to the remaining parts.

In which case, the answer for (f) is

The point 6 is at a lower energy compared to the TE4 and when we look at the full energy distribution, point 6 is the lowest energy which means that it is the most stable configuration that a particle can have. However, the particle before 6 is vibrating upwrds and the particle after 6 is vibrating downwards. Since these points are intermediate and have higher energy compared to the stable configuration, particles can have TE4 momentarily i.e., they will not exist in this energy state. So due to the availability of a global minimum energy configuration very near by the particles will not exist in TE4.

Please comment if you have doubts. Thanks.

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