- #1
RedMech
- 13
- 0
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
du/dr=o at equilibrium distance, ro
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?
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
Homework Equations
du/dr=o at equilibrium distance, ro
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: