Answered: One model for the potential energy of a…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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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.

r_eq= ?

F_r(r_eq+r₁)= ?

K(r_eq)= ?

(NOTE: these are all part of the same question)

I got .957026 nm for r_eq, and -1.4348 eV/nm for F_r(r_eq+r₁), and I couldnt get an answer for K(r_eq). 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) = Uo[(÷)1² – ()1
where ro = 0.65 nm and Uo = 7.4 ev,
Note: 1 ev =1.6 x 10-19 J.
Some helpful units:
[Force] = eV/nm
[Energy] = ev
[distance] = nm
Equilibrium Distance
Force
KineticEnergy
AddedConstant
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(x0) = 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) = Uo[(ro/r)² – (ro/r)*] + U1
where U = 4.5 eV, reanswer all of the previous questions using this new potential energy function.
Click here for a hint
Teg=.957026 nm
F,(req + r1)= -1.4348 eV/nm
K(req)=

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