Hints for Assignment 1
Problem 2
The force, F = dE/dr. then (from class and from the book)
A B
EN = ! + n = EA + ER
r r
dE N A nB
FN =
= 2 ! n+1 = FA + FR
dr
r
r
The attractive force, FA =
A
, (from class and from Figure 2.8a)
r2
From the book (page 31):
A=
(Z1e)(Z 2 e)
(Z e)(Z 2 e)
, then FA = 1
4"# o
4"# o r 2
Z1 = Z 2 = 2, # o = 8.85x10 !12 farads / m, e = 1.602x1019 Coulombs, r = 1.25x10 !9 m (given)
farad =
(Coulombs)2 C 2
=
Joule
J
Then solve for FA (recall J = Nm)
Problem 3
The net potential energy between two atoms is (from class, and from above):
The bonding energy, Eo, is the minimum on the energy vs. separation distance curve (Fig. 2.8b). This is
when the atoms are in equilibrium, in their lowest energy state.
You know the equation, to find the minimum, take the derivative and set it = 0.
A B
+
r rn
dE N A nB
= 2 ! n+1
dr
r
r
EN = !
When dE N /dr = 0, r = ro , then
A nB
=
ro2 ron+1
Then solve for ro
To find E o , substitute the expression for ro into
A B
Eo = ! + n
ro ro