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!

Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium sep

  1. Aug 11, 2011 #1
    Problem:
    The adjacent lines in the pure rotational spectrum of 35CI19F are separated by a frequency of
    1.12 x 1010 Hz. What is the equilibrium separation of the atoms in this molecule?

    The attempt at a solution

    So, the equation I think I need to use to find the equilibrium separation is I = [itex]\mu[/itex]r02
    But I don't know how I can find the inertia,as I don't know how the frequency and inertia are linked?
     
    Last edited: Aug 11, 2011
  2. jcsd
  3. Aug 11, 2011 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    The emitted or absorbed photon energies differ by ΔE=[STRIKE]h[/STRIKE]2/I. How is the photon energy related to frequency?

    I is the moment of inertia of the diatomic molecule: I=r2m1m2/(m1+m2), where r is the distance between the atoms.

    ehild
     
  4. Aug 12, 2011 #3
    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    Thank you!

    Ok, so I've tried using [itex]\Delta[/itex]E = [STRIKE]h[/STRIKE]/I

    and to find [itex]\Delta[/itex]E, [itex]\Delta[/itex]E = hf

    and then just number crunching that all through, using m1 = 35 and m2 = 19,

    I get r = 1.1 x 10-6m

    Is that right? It seems pretty big?
     
  5. Aug 12, 2011 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Last edited: Aug 12, 2011
  6. Aug 12, 2011 #5
    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    Yes, does help if I look at my notes properly.

    Working that through I get r = 1.1 x 10-23m
     
  7. Aug 12, 2011 #6

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    Can you show your calculations in detail?

    ehild
     
  8. Aug 12, 2011 #7
    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    [STRIKE]h[/STRIKE] = h / 2[itex]\pi[/itex] = 1.055 x10-34 Js

    [itex]\Delta[/itex]E = hf = h x 1.12 x1010 = 7.4256 x10-24

    I = [STRIKE]h[/STRIKE]2/[itex]\Delta[/itex]E
    = 1.113 x10-68 / 7.4256 x10-24
    = 1.520 x 10-45

    r = [itex]\sqrt{1.520x10-45/12.314}[/itex]
    = 1.1 x10-23m
     
  9. Aug 12, 2011 #8

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    What is the reduced mass? Did you take it 12.34 kg? Is the mass of a molecule in the range of kg-s?
     
  10. Aug 12, 2011 #9
    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    That's what I've taken it as, yes. I realise now how stupid that is but I don't know how to work out the mass from the numbers. I don't even know what the numbers are next to the elements.
     
  11. Aug 12, 2011 #10

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    Those numbers are the "molar" masses, the mass of one mole of atoms in gram unit. How many atoms are there in one mole?

    ehild
     
  12. Aug 12, 2011 #11
    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    6.02 x 1023?

    Do I need to divide the value of [itex]\mu[/itex] by that?
     
  13. Aug 12, 2011 #12

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    Yes.

    ehild
     
  14. Aug 12, 2011 #13
    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    Is the right answer 8.62 x 10-12m?
     
  15. Aug 12, 2011 #14

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    Not yet. 12.34 is the molar mass in grams, so divided by the Avogadro number, you get μ in grams, but you need it in kg-s in the equation.

    ehild
     
  16. Aug 13, 2011 #15
    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    2.72 x10-10m?
     
  17. Aug 13, 2011 #16

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Re: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium

    It is OK.

    ehild
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Molecular Rotation - Adjacent lines in pure rotational spectrum: find equilibrium sep
Loading...