1. Not finding help here? Sign up for a free 30min 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!

Energy of a Hydrogen Flouride molecule in normal mode vibration

  1. Nov 18, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi everyone! first post here :)

    Basically, the question is as follows:
    Consider a hydrogen flouride molecule (atomic mass of H is 1g/mole and of F is 19 g/mole).
    1. Write the energy of the system in terms of the displacements of both atoms.

    There are other questions but if i can get this one I think the others will be fine.


    2. Relevant equations
    This is a coupled oscillator problem, so we're gona model it as two masses with a spring in between, that has a stiffness k. the equations are:
    Total energy E = 1/2 kx2
    General solution to the coupled oscillator differential equation: x = A cos(ωt) (we dont have to worry about phase shift)
    Restoring force F by Hooke's law = -kx

    3. The attempt at a solution

    What I'm having trouble with is 2 things:

    1st of all - my professor has written in his reference notes that the total energy E of another similar problem is 1/2 kx2. Shouldn't it be 1/2 kA2; the sum of 1/2 mv2 and 1/2 kx2?

    secondly - Im a bit confused as to how I'm meant to work with the displacements - since each atom displaces in the opposite direction (I don't think there is any normal mode other than this one) how do i construct the problem? Anyway, here's what I got for a solution but I have no way of telling if its right since its an assessed assignment:

    If we consider the displacement of the hydrogen atom as xH and that of the fluoride atom as xF then:

    E = 1/2 kx2 = 1/2 k(xH-xF)2

    So...here's the confusion now...the signs of the displacements xH and xF...what are they? @_@ and is the equation im using even the right one?

    Thanks a lot guys!
     
  2. jcsd
  3. Nov 18, 2012 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Hi Dixanadu, welcome to the forum.
    Pedantry point: I believe it's "fluoride".
    Yes.
    You know that the mass centre of the system won't change. That gives you a relationship between the two displacements. The extension of the 'spring' will be their sum.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Energy of a Hydrogen Flouride molecule in normal mode vibration
Loading...