Unravelling the Separation of 35CI19F Atoms: A Problem Solved

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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 = \mur02
But I don't know how I can find the inertia,as I don't know how the frequency and inertia are linked?
 
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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
 


Thank you!

Ok, so I've tried using \DeltaE = [STRIKE]h[/STRIKE]/I

and to find \DeltaE, \DeltaE = 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?
 


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

Working that through I get r = 1.1 x 10-23m
 


Can you show your calculations in detail?

ehild
 


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

\DeltaE = hf = h x 1.12 x1010 = 7.4256 x10-24

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

r = \sqrt{1.520x10<sup>-45</sup>/12.314}
= 1.1 x10-23m
 


What is the reduced mass? Did you take it 12.34 kg? Is the mass of a molecule in the range of kg-s?
 


That's what I've taken it as, yes. I realize 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.
 
  • #10


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
 
  • #11


6.02 x 1023?

Do I need to divide the value of \mu by that?
 
  • #12


bmarson123 said:
6.02 x 1023?

Do I need to divide the value of \mu by that?

Yes.

ehild
 
  • #13


Is the right answer 8.62 x 10-12m?
 
  • #14


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
 
  • #15


2.72 x10-10m?
 
  • #16


It is OK.

ehild
 
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