Homework Help: Bonding in Solid State Physics

1. Nov 17, 2013

RedMech

1. The problem statement

The potential energy between two ions is
u(r) = -α/r2 + β/r8

Determine:

(i) The intermolecular distance ro for which the potential energy is minimum
(ii) The inter-atomic distance for which the potential energy is zero is

R= (2)-1/6ro

2. Relevant equations

du/dr=o at equilibrium distance, ro

3. The attempt at a solution

i) du/dr= 2α/r3 - 8β/r9 = 0 at equilibrium distance ro

we end up with

ro = (4β/α)1/6

ii) -α/r2 + β/r8 = 0

which give us

R-6 = α/β

We can express the ratio α/β interms of ro so that

R-6 = 4ro-6

and finally

R = (4)-1/6ro

My question now is why does my answer have a 4 instead of a 2 in it?

Last edited: Nov 17, 2013
2. Nov 17, 2013

ehild

Your result is correct, and it can be written also as R=2-1/3 r0.

ehild