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.
• 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. Giving the
ball a little kinetic energy — enough to get it over the hump in the middle — would let it roll into the
deeper well, gaining a lot of kinetic energy in the process. You can go from one bound state to a more
deeply bound one and get some additional energy (in this case kinetic) 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.)

The decomposition of one mole of water molecules into H2 and O2 molecules requires the input of 113
Cal.

Explanation / Answer

The decomposition of one mole of water molecule into H2 and O2 molecules requires the input of 113 cal requires is analogous to the curve f3. This is because water molecule is in a bound state. Giving an energy of 113 cal will break the bond between the hydrogen and oxygen.

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