A variety of interesting behaviors can be described with different shapes of pot

Question

A variety of interesting behaviors can be described with different shapes of potential energy. Four qualitatively different PE shapes are shown in the figure below. In each figure, the horizontal axis is a position and the vertical axis is a potential energy. You can think of them as frictionless tracks with a small ball rolling on them. The energy they describe is like a gravitational potential energy of the ball. In this problem, we will neglect the repulsion between atoms when you try to push them too close together. Instead, we will assume they can just be pushed through (or past) each other. Thus, both ends of the graph - large positive and large negative x- represent the atoms being far apart. The graph labeled F1 is a hill and represents an unstable equilibrium. A ball can sit at the top of this hill, but a small deviation from the exact center will lead to forces that will cause the ball to roll down the hill and convert the potential energy to kinetic. The graph labeled F2 is a hill with a dip and represents a metastable state. If a ball is sitting in the center of the dip at the top, a very small deviation will just oscillate back and forth a tiny bit. But if you provide the ball with just a bit more of kinetic energy, it will have enough energy to go up over the lip of the inner dip and roll down the long hill, gaining lots of kinetic energy in the process. The graph labeled F3 is a well. When the ball is at the bottom of the well, it is a bound state. You have to give the ball kinetic energy equal to the depth of well to get it out. If you do that, when it gets out, it would have 0 kinetic energy left, using it all up in climbing out of the well. The graph labeled F4 is a double well. Suppose the ball is at the bottom of the left well. If we temporarily lend the ball enough kinetic energy to get it over the hump in the middle (an activation energy)- it could roll freely into the deeper well on the right. Then, taking the energy back that we had just lent the ball to get over the hump, we could trap the ball in the right well. The ball is now at the same total energy as it had before, but is in the right well. In that right well the ball has a lot of kinetic energy as it passes the lower dip than it had when it was in the left well. It could give that energy up (through a collision or emitting a photon) and come to rest in the bottom of the second well. This is how you can go (with a little bit of help from your friends) from one bound state to a more deeply bound one and get some additional energy out as a result. Some of these situations are analogous to the situation of chemical bonding. Consider the following examples and discuss which if any of the potential energy shapes provide a useful analogy. Explain why you think so. (The energy going into or coming out of a chemical reaction may be in the form of kinetic energy - seen as heat - or in terms of electromagnetic energy - a photon.) Two moles hydrogen atoms may interact and form a mole of H2 molecules. When they do so, they release 103 Cal (kcal). Decomposing one mole of water molecules (H20) into its component atoms requires the input of 220 Cal. The decomposition of one mole of water molecules into H2 and O2 molecules requires the input of 113 Cal. The phosphorus in the head of a match burns in air, giving off energy when you strike the match.

Explanation / Answer

1. H + e- ? H- + h?
H- + H ? H2 + e-

this is an exothermic reaction which is giving a photon . this actually happens in nebula and interstellar clouds so it is similar to F1 like the ball giving out kinetic enegy from potential energy without a push

3. Decomposition of water molecule is similar to F3 because the water molecule is stable so it possess great potential enrgy so energy is to be supplied to that inorder to decompose it. but the chemical reaction itself doesn't involve any release of energy . so it is like the ball comes out of well but has no kinetic energy

2. There is a reason to explain this after 3rd . this is similar to F2 but a combination of 1 and 3 beacuse electrolysis of water and breaking the bonds is the initial push to be given as energy but the resulting reaction involves generation of huge amount of energy in form of heat and light

4. burning of match involves a similar analogy to F4 because in match stick before burning the red phosphourous is present in the head which is like at bottom of left well. when we supply energy in form of frictional heat it converts to white phosphourous which is like going to right well but white phosphourous burns when exposed to air then it is like object having a great kinetic energy at the bottom but the reaction goes as

P4 + 5 O2 ? 2 P2O5

Diphosphorus pentoxide is extremely hygroscopic and quickly absorbs even minute traces of moisture to form liquid droplets of phosphoric acid:

2 P2O5 + 6 H2O ? 4 H3PO4

Now it is in stable state with high potential energy so it is at bottom of right well

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