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- Homework Statement
- I have done most part of the data analysis. I am stuck with rearranging the equation in the correct way.

- Relevant Equations
- see below

Hey!

I am trying to determine the bond length of acetylene by analysing the vibrational spectrum of both H-Acetylene and D-Acetylene. I was able to calculate both the rotational constant and the moment of inertia but am stuck now as to how I get to the correct solution.

On the left is the original moment of inertia equation for polyatomic molecules which I have expanded to be specific for acetylene.

Then, on the right side are my rearrangements for the bond length of the respective molecules. I have been told that this is solvable by using two simultaneous equations - the moment of inertia for H and D. But I don't know how to solve this in practice.

However, I have been told that this is (probably) the correct equation. But I don't know how I get to this point.

I understand that the basic rearrangement equals r = √(I/2m) but, for example, I don't know why r(D) - r(H) would equal r(H) if that's what the first equation implies?

Hope that's not too confusing.

Thanks!

I am trying to determine the bond length of acetylene by analysing the vibrational spectrum of both H-Acetylene and D-Acetylene. I was able to calculate both the rotational constant and the moment of inertia but am stuck now as to how I get to the correct solution.

On the left is the original moment of inertia equation for polyatomic molecules which I have expanded to be specific for acetylene.

Then, on the right side are my rearrangements for the bond length of the respective molecules. I have been told that this is solvable by using two simultaneous equations - the moment of inertia for H and D. But I don't know how to solve this in practice.

However, I have been told that this is (probably) the correct equation. But I don't know how I get to this point.

I understand that the basic rearrangement equals r = √(I/2m) but, for example, I don't know why r(D) - r(H) would equal r(H) if that's what the first equation implies?

Hope that's not too confusing.

Thanks!