Rotating diatomic - Pretty basic first year question. Workings given

[elemis]

Part v is where I'm stuck.

All relevant equations and the bit where I'm stuck are in the second attachment with my workings

 

[elemis]

If I can find the value for L I can substitute it into the equation for L=Iw and using the known I value I can calculate w and hence the frequency (2pif=w).

 

[tiny-tim]

hi elemis!

why are you making it so complicated?

finding ω is a straightforward centripetal acceleration question! ​

 

[elemis]

hi elemis!

Why are you making it so complicated?

finding ω is a straightforward centripetal acceleration question! ​

i goooot itt ! Woooohoooooo ! Thank you !

 

[Nickie]

Hi there,

Thank you for sharing your question and your workings with me. It seems like you have a good understanding of the basic concepts involved in solving this problem. I will try my best to help you with part v where you are stuck.

Firstly, let's review what we know about rotating diatomic molecules. A diatomic molecule is one that consists of two atoms bonded together, such as HCl or O2. When these molecules are in a gas phase, they are free to rotate about their center of mass. The rotational motion of a diatomic molecule can be described using the moment of inertia, I, which is a measure of an object's resistance to rotational motion.

In your problem, you have been given the moment of inertia of a rotating diatomic molecule, I = µr^2, where µ is the reduced mass of the molecule and r is the bond length between the two atoms. This equation is derived from the more general equation for moment of inertia, I = mr^2, where m is the mass of the molecule.

Now, in part v of the problem, you are asked to find the moment of inertia for a rotating diatomic molecule made up of two different atoms, A and B, with masses mA and mB, and bond length r. To solve this, we need to use the concept of reduced mass, which takes into account the masses of both atoms in the molecule. The reduced mass, µ, is given by the equation µ = (mA*mB)/(mA+mB).

Substituting this value of µ into the equation for moment of inertia, we get I = µr^2 = ((mA*mB)/(mA+mB))*r^2. This is the moment of inertia for a rotating diatomic molecule made up of two different atoms.

I hope this helps you understand how to solve part v of the problem. Please let me know if you have any further questions. Keep up the good work!