9 DL FNTs 4) Look at a plot of the atom-atom potential. If the two atoms are momentarily at rest with a center to center separation of 1.4 sigma, what is the total energy of the system? If the sytem is at rest, it means one of three things. It could mean that this system isn't moving at all, that it is sitting at equilibrium, at rest. Since we're saying its at rest at 1.4 sigma, this isn't the case. The other two cases are when two masses are moving relative to one another. One case is when the bond between the atoms is compressed, and the atoms are momentarily at rest before moving away from each other. This occurs at values of r less than the equilibrium length, less than 1.12 sigma, so we know that's not the case. The third case is when two atoms are as far apart as they can get before they're pulled back together by their bond, when PE is equal to total E, and KE is zero. This occurs at some rmax greater than 1.12 sigma. This must be the case! The total energy doesn't change, because this is a closed system, and since we know that at 1.4 sigma, Etot is equal to PE, we can say that Etot is equal to that same value everywhere. 5) With respect to the plot of the atom-atom potential, what is the meaning of the following quantities: r0, rmax, rmin? How are they different or similar to r? ro is the equilibrium length between the centers of the atoms, which corresponds to the lowest point on the potential energy curve. It's the distance between the atom centers when the atoms are at rest, not compressed or stretched. We can figure out rmin and rmax for a specific total energy value. If we have some total E greater than the well depth, than our atoms are oscillating, and the distance between their centers is expanding contracting. and rmin is the smallest distance between the atoms, when they've gotten as close as they can for that total E. rmax is the farthest away they can get while oscillating. r0, rmin, and rmax are numbers, while r is a variable that defines our x axis, it's the distance between the center of the atoms. 6) What is the difference between a pair of atoms that are bound, and a pair of atoms that are unbound? How can you tell whether a pair of atoms are bound or
unbound? A pair of atoms that are bound have a bond between them, an unbound pair have no bond. Atoms in the solid or liquid state are bound, and atoms in the gas state (monatomic, at least) are unbound). You can tell whether a pair of atoms are bound or unbound based on their total energy. If their total energy is negative, they are oscillating around some bond, because they are bound. If a pair of atoms have total energy equal to zreo, or positive energy, then they are unbound. 7) What is the difference between delta E, E, and Eavg? Delta E is the way that energy has changed from some initial point to some final point. Delta E = Efinal - Einitial, we don't care how it happened, only how we began and how we end. Delta E is a change in energy. E is a value of energy at a certain point, or at a certain temperature. A closed system will have a total change in energy of zero, but some finite total energy value at any point. Eavg is the average energy for a system, which is found by taking the energy values over a span of time and averaging them. For a mass spring, the average KE and the average PE are equal, they are both half of the Eth on average, but at any point you could have a PE value equal to Eth and a KE value equal to zero, or vice versa.