1) On model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is 12 Ⓒ² - 0

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1 On Model For The Potential Energy Of A Two Atom Molecule Where The Atoms Are Separated By A Distance R Is 12 0 1 (362.11 KiB) Viewed 34 times

1) On model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is 12 Ⓒ² - 01 U(r) = Uo a. (3 points) What units should U₁ and ro have? b. (3 points) Sketch a graph of this potential energy function, assuming r > 0. c. (4 points) Show that the distance between the atoms when the molecule is in stable equilibrium is given by req = 21/6 ro d. (3 points) If the distance between the atoms increases from equilibrium to r = 31/6 ro. Show that the force from one atom on the other associated with this potential energy is given by 20⁰ Ẻ : 37/6r0 e. (3 points) Assume the atoms are oscillating so their maximum separation is the same as described in the previous part, max 31/6ro. This will be one of the turning points on your graph for the potential energy function. Go to the sketch you made in part (b.) and indicate this turning point as well as the other turning point on your graph. ↑ = (¹/6 ro. To f. (3 points) Show that the other turning point will occur at r = help you with this, I would recommend that you introduce a variable called ß = (). You will then be solving a quadratic equation for ß. For the special case of the max that we are using, you will not end up needing to use the quadratic formula in solving for ß as your equation can be factored. g. (3 points) Show that the maximum kinetic energy of the system will be given by = U₁ KEmax 36 h. (3 points) If the molecules begin at rest with r = ro, what would be the eventual fate of the molecule? As a hint, you should go back to your graph to help you answer this question.