Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
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Chapter 7, Problem 50P
In ionic solids such as NaCl (salt), the potential energy of a pair of ions takes the form U = b/rn – a/r, where r is the separation of the ions. For NaCl, a and b have the SI values 4.04 × 10−28 and 5.52 × 10−98, respectively, and n = 8.22. Find the equilibrium separation in NaCl.
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P6
The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by U(x) = −a/x12 − b/x6 where x is the distance between the atoms. (a) At what distance of seperation does the potential energy have a local minimum (not at x = ∞)? (b) What is the force on an atom at this separation? (c) How does the force vary with the separation distance?
The potential energy of two atoms in a diatomic molecule can be approximated by the Lennard-
Jones potential U(r) = a/r¹² — b/r6, where r is the distance between the two atoms, and a and b
are positive constants.
a) Find the force F(r) on one of the atoms as a function of r.
b) Find the equilibrium distance between the two atoms. Is this equilibrium stable?
c) Suppose the distance between the two atoms is equal to the equilibrium distance found in part
b). What minimum energy must be added to the molecule to break the two atoms apart? (This
is called the dissociation energy of the molecule.)
Chapter 7 Solutions
Essential University Physics (3rd Edition)
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