Binding Energy of the Hydrogen Molecule when two hydrogen atoms of mass m combine to form a diatomic hydrogen molecule (H2), the potential energy of the system after they combine is -fl., where fl. is a positive quantity called the binding energy of the molecule.
(a) Show that in a collision that involves only two hydrogen atoms, it is impossible to form an H2 molecule because momentum and energy cannot simultaneously be conserved. (Hint: If you can show this to be true in one frame of reference, then it is true in all frames of reference. Can you see why?) (b) An H2 molecule can be formed in a collision that involves three hydrogen atoms. Suppose that before such a collision, each of the three atoms has speed 1.00 x l03 m/s and they are approaching at 1200 angles so that at any instant, the atoms lie at the comers of an equilateral triangle. Find the speeds of the H2 molecule and of the single hydrogen atom that remains after the collision. The binding energy ofH2is fl. = 7.23 X l0-19 J, and the mass of the hydrogen atom is 1.67 X lO-27 kg.