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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One model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is
U(r)=U0[(r0/r)12−(r0/r)4]
where r0 = 0.65 nm and U0 = 7.4 eV.Note: 1 eV = 1.6×10−19 J.Some helpful units:[Force] = eV/nm[Energy] = eV[distance] = nm
Here is what I am having trouble with:
You can choose where the potential energy equals zero anywhere you want (you can add or subtract any constant to it). For this function, U(∞) = 0. This is very common for electromagnetic problems like you will see in Physics 2. If the potential energy function were defined as
U(r)=U0[(r0/r)12−(r0/r)4]+U1
where U1 = 4.5 eV, reanswer all of the previous questions using this new potential energy function.
req= ?
Fr(req+r1)= ?
K(req)= ?
(NOTE: these are all part of the same question)
I got .957026 nm for req, and -1.4348 eV/nm for Fr(req+r1), and I couldnt get an answer for K(req). My answers are wrong. Where am I not understanding?
One model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is
U(r)=U0[(r0/r)12−(r0/r)4]
where r0 = 0.65 nm and U0 = 7.4 eV.Note: 1 eV = 1.6×10−19 J.Some helpful units:[Force] = eV/nm[Energy] = eV[distance] = nm
Here is what I am having trouble with:
What is the distance between the atoms when the molecule is in stable equilibrium?
If the distance between the atoms increases from equilibrium by r1 = 0.2 nm, then what is the force from one atom on the other associated with this potential energy? (Enter your answer as postive if they repel each other, and negative if they attract.)
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?
Chapter 7 Solutions
Essential University Physics (3rd Edition)
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