Question

1. In a high temperature experiment an ozone molecule, O3, moving right at 1.5 × 103 m/s, collides head-on with an oxygen molecule, O2, which is moving to the left at 400 m/s. Both of these velocities are for the molecules viewed from the Earth frame. No chemical reaction takes place but the ozone becomes “vibrationally excited” during the interaction so that its internal energy increases by 1.4 × 10−20 J. You will need the inertias of the molecules, but you can look up the inertias of O2 and O3 molecules yourself. The collision takes place in gas phase, so the nearest other molecules are very far away compared with the size of the molecules. Molecular scale collisions like this take place in extremely short times (of order 10−15 s is fairly typical).

(a) Is the system of the O2 and O3 molecules isolated? Explain.

(b) Is the system of the O2 and O3 molecules closed? Explain.

(c) What kind of collision is this (elastic, inelastic, totally inelastic, explosive separation)? Explain.

(d) Find the center of mass velocity of the system, then transform the velocities of the molecules into the center of mass frame. (e) Find the velocity of the ozone molecule after the collision, in the Earth frame.

(f) What is the minimum relative speed of the two molecules that would allow it the ozone molecule to be excited into this vibrational state with Eint = 1.4 × 10−20 J?

Answer 1