Question

V „j(r) = 4€[(9)2 – (9)) a. Give the units of o and ε. b. Find the force, as a function of o and ε, on an atom with the following potential if the atom is at a distancer = o from the nucleus of another atom: (F = - dr.). c. An atom A rests in the middle of two other atoms, B and C, so that all three atoms lie on the same line. Atom A is a distance o from atom B and a distance 20 from atom C. If all three atoms have the same value for o and ε (all three atoms are identical), find: i. Find V 1 total for atom A as a function of ε. (Recall that V obeys superposition; that is, V LJ total = V B+V). Which force is repulsive? Which force is attractive? Assuming atom A starts at rest, will atom A move towards atom B or atom C? Find |F I total | for atom A as a function of o and ε. (Force also obeys superposition, but be careful: force is a vector and has direction) 11.

Answer 1

Ans a) The unit of $\sigma$ is Meter(SI) or Angstrom and of $\varepsilon$ is joule/mole.

Ans b and c in images
Ans b - To find the folce as functun of o 82 for Leanead Jones potenti al. at clistan ce r=o objective Given that = F= -dv dr Vis cr) = 4E Hence , substtuting eq @ in o 8 followed by differenteation [66)]a] F=4E F - -4E -12 r13 focks. Taking -12 Ge as commin F = 48E ( 0.566 - r13 r7 So, The force betuween the tuo particle os per Leanerd Jones potential. es 12. F= 488 (9 y13 0.566

Ans bJ Ccontinued, Now subathuting r=6 (as per the feloblem) F = 48E (olk 0.5 66 r13 77 - 48€ ( -05 ) = 48€ (+-0-5) - 0-5 6 13 24E61 24E

Ano c> Given - Distance blw A & B=6 -A& c = 26 8 all thiee atonus are iclenticels (same E &) Subpout o VIJ Cate) = fol (A) So, substihaung the values in V. CA6) for B Va trme faE[E" (4*] + a€[($}*-($J']] VeJ CTolal) = + 4E[1$)"-(E)']] = 4€ [($)"- (5)']+ 4€ [ E)*- (E)') = 4E [ie_ 1^] + 4ɛ [ "-E! 0.000244 - 0.015625] o+ 4E[-0.015391 - - 0.661524E - -0.061524E Subport Force betuem A&B = Fas = 488 [-05) 0.506 r7 7-7-) 38 = 24E/ o2 24E-| - 3 84 =

And 3 subpot D force belueen A &C = F= 48€ro12 13 0.566 o12 = 48E - 0.5 56 (20/13 (25)7) = 48E (-) co.00o- = 48€ .00230 62) 0.0001220 - 0.00 = 48 E (-0.0037842) = - 0.1816416 or -0.1816416 Eo-1 So the total folee betuem FAB & Fue FAB T FAc - 24667 + (-0.1816416E6) = 23.818354 E So, the foce on Atom A es 1 23.818 Eo-I Ans s subbart Force beturenn A&C = Folce betueeenA&B- attractue repulsine Ajwed move to worels B. Hency