1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

[PoM] Lennard-Jones potential parameters

  1. Nov 24, 2016 #1


    User Avatar

    Hi guys! I need your help!

    1. The problem statement, all variables and given/known data

    Use the function of Lennard-Jones V (R) = ε [(σ / R)12 - (σ / R)6] as model for the adiabatic potential energy in function of the separation between the 11B boron and nitrogen nuclei 14N. You determine the parameters ε and σ to reproduce the spectroscopic values of the vibrational quantum, ν = 1514.6 cm-1, and the separation of 1,666 cm-1 between the lines of rotational BN molecule.

    3. The attempt at a solution

    I have

    ΔErot2/I=1.666 cm-1=3.3091*10-23 J I=ħ2/ΔErot=3.3603*10-46 Kgm2


    R0=√(I/μ)=1.8125*10-10 m

    At this point, I calculating the minimum oh the potential:

    V(0)=∂V(R)/∂R =0 ⇒ R06=2σ6 ⇒ σ=6√(R06/2)=1.6147*10-10 m

    For ε, I calculating k by:


    but here I'm lost...

    Who can help me? Please!
  2. jcsd
  3. Nov 24, 2016 #2


    User Avatar

    Staff: Mentor

    You need an equation to relate k to ##\nu##, then the only unknown in there will be ε.
  4. Nov 24, 2016 #3


    User Avatar

    Tanks for your answer,
    the only equation i know to relate k to ν is:


    so, i have (using R=R0):


    but is dimensional incorrect...
  5. Nov 24, 2016 #4


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    When you let R = Ro, you should then be able to simplify to get a nice expression relating ##k## to ##\varepsilon## and ##\sigma##. This might make it a little easier to get the correct expression for ##\varepsilon## in terms of ##\nu##.
    Last edited: Nov 24, 2016
  6. Nov 24, 2016 #5


    User Avatar
    Homework Helper
    Gold Member
    2017 Award

    I think your expression for ##\varepsilon## is correct except that you appear to be off by a factor of ##\sigma##. Try to simplify the expression as much as possible.
  7. Nov 24, 2016 #6


    User Avatar

    Oh Damn!
    yes, the equation is correct (apart the simplifications), but υ must be convert to m-1 and not to J!


    ε=[μ(2πcν)2σ2(6√2)14]/72=1.5192*10-18 J

    Now it's ok!

    Tanks at all!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Lennard Jones potential Date
[PoM] Cohesive energy in an argon crystal Dec 5, 2016
Lennard-Jones potential minimized Feb 17, 2015
Lennard-Jones potential . Jan 22, 2015
Linear compressibility Lennard-Jones potential Aug 11, 2014
Lennard-Jones Potential May 8, 2010