Prerequisites:
- Interatomic forces
- Bound states
- Going to a deeper well
When two atoms are bound in a molecule, the interaction between them can sometimes be modeled by a force that is attractive at long distance and repulsive at short. This interaction can be described by a potential well that looks like the figure at the right. (See Interatomic forces.) The horizontal axis in this graphs represents the distance between the atoms' centers. When the atoms are in a bound state, the point on the graph representing the relative position of the atoms will be near the bottom of the well. The higher up it is, the more that atoms will oscillate around their stable point (the minimum of the potential well).
A. The CLUE simulation of molecular collisions shows the potential energy between two bound atoms moving in a gas with other atoms. When the simulation starts, the two bound atoms (shown darker than the others) are bound with a relative energy near the bottom of the potential well describing the interaction between them. As they move around, they may collide with other atoms or molecules and some of the kinetic energy of the other atom may be transferred through the collision into the relative motion of the two bound atoms, setting them oscillating.
Consider two situations: one in which the collision adds not enough energy to the relative motion of the two bound atoms to separate them and one in which it adds more than enough to separate them. For both cases, tell the story of what is happening to the relative motion of the two atoms and describe how that motion and change in motion would be represented on the potential energy graph of the relative motion of the two bound (at first) atoms.
B. In the problem, Going to a deeper well, we considered what it might mean for a system moving in a double potential-energy well like the one shown at the right. For atomic/molecular physics, this kind of a potential energy curve might represent the potential energy of a more complex molecule of atoms in two different arrangements. The variable "x" now does not just represent the distance between two atoms, but may be a more complex combination of coordinates (a "reaction coordinate") that describes not only the separation of the atoms but their arrangement. Here, we will consider positive values of x to represent one arrangement and negative values a different one. In which arrangement -- x positive or x negative -- is the set of atoms more strongly bound? Explain why you think so.
C. Now suppose that the molecular system starts in the arrangement represented by the well at the right (positive x) as shown by the solid black horizontal line in that well. Then suppose that as a result of a collision with an atom, the molecule makes a rearrangement to the state shown by the black horizontal line in the well at the left (negative x). The transition is indicated by a blue arrow.
Given that total energy (potential plus kinetic) of the entire system (molecule plus atom) is conserved, do you think that the atom would leave the collision with this molecule going faster than when it came into the collision, slower, or going at the same speed? Explain why you think so.