Question

1. (This problem is similar to Problem 5-2 in McQuarrie and Simon) Make the "harmonic approximation" to the following diatomic potential energy function to obtain k the corresponding harmonic potential energy function of the form Vi0(R) =^(R-R) as illustrated in the figure below. Find expressions for the harmonic force constant k and equilibrium internuclear distance R in terms of the parameters of the potential function, and clearly identify them as your answers. The potential is the Lennard-Jones Potential 12 |+d VL(R) 4d This potential is used to approximate weak attractive interactions between atoms that are not covalently bonded, like Ar2. Hint: start by showing that the minimum of the potential function occurs at an internuclear distance of 20. VL(R) 2.0 15 1.아 0.5 R 0 2 3 4 st

Answer 1

Answeri The potential is the lennard -- Jones Potential Ves (8) = 42 43*2*1* d The minimum of the potential function occurd for de - af eget the good (or) Rew = 200 [128 13012 - 6x70 Also dVLJ (R)] = 4d dR? Leen , Revi' brew 156012 - 42 = 4 d 1 fea 1 Real sked 420] Scanned with CamScanner

72 dl 2 15.02 = 57.15% R = Rew Now Taylor expanding Ve JCR) about on obtains (retaining upto gieacoatic termos ) Vizce) – Van (Raw) + dorm Cre-Rew) + + , CPL CR - few) to 24(63.)-41 doo 79d thx 5,43 021 x IR-Rowl ya 21 where Cs Scanned ariel = 4K (R - Rem)? kan220] Rex egy o CamScanner