Essential University Physics
4th Edition
ISBN: 9780134988559
Author: Wolfson, Richard
Publisher: Pearson Education,
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Chapter 7, Problem 52P
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.)
In another two-atom molecule that is breaking apart, the force from one atom to the other is given by
F12= F0(r/r2)e^-(r/r2)^2
where F0 = 15.6 eV/nm and r2 = 2.2 nm. Find the change in potential energy of the molecule due to this force if the separation of the atoms changes from r = 2.5 nm to r = 4.1 nm.
Chapter 7 Solutions
Essential University Physics
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