Question

The Lennard-Jones potential energy Ulj(x) is important in chemical bonding theory and is given by 1012 ool ULJ 1 1 1 ULJ = 4€ | (x12 26 I 0 E 012 where e and o are constants and ř=r/o. (a) Sketch a graph of this potential energy. (b) Use IDL to obtain a careful graph of ULJ(x)/€ versus x/0. (c) Locate any equilibrium points, (d) determine which ones are stable, and (e) find the frequency of small oscillations about about any equilibrium point that is stable.

Answer 1

-ARUNS PAGE NO. DATE : Vander walls a potential energy V=YELLOW 19)"] for maxima & minima 6 driol da /r=ro = 0 = 4 folt 2017 7 813 Jr=ro 1= 2006 rogol 1906 potinhal energy and so How wonder watt r = 460) - a tot 1 V(76) = 4 folt ] 46[-+ ++] -4601 -2*+) = 4x+y=- Ivero) = - to s aver) port there altruction = Repulsion part . 6

In that gabore figure minima , we at r=ro & Vly=-to , we have minima, called are a stable point. de weg 46. [-ya ora nyoyo y = vliv v"(ro) 42 + 154(124156x4] Villero y = [-42 + 7) = 30 (30] - home (O) = 57.14616 Angular frequency of mors m., w=lvieros fog littery frequency o = tad vilon Detta 5714603