One dimensional diatomic lattice oscillations

[PsychonautQQ]

Suppose we allow two masses M1 and M2 in a one dimensional diatomic lattice to become equal. what happens to the frequency gap? what about in a monatomic lattice?
Knowing that (M1)(A2) + (M2)(A1) = 0

 

[DrDu]

a) is this homework?
b) what are A1 and A2?

 

[PsychonautQQ]

it's one of those "test your knowledge" questions at the end of the chapter, not homework X_x but I've been trying to figure it out on my own and can't. A1 and A2 are amplitudes

 

[DrDu]

I don't know what you were shown in that book, so I am not sure about what they expect you to do.
Qualitatively, what kind of oscillations do you expect in a chain made up of, say, H2 molecules (atoms of equal mass but different inter- versus intramolecular distances)?

 

[Anon0123]

Hey Psychonaut, I know this is probably coming too late, but I had to answer the same question recently on homework lol. Assuming you are also using Omar's book on solid state physics, refer to page 98. Here we see that the frequency gap between the optical and acoustic modes can be defined as (2α^2/M1)^(1/2) - (2α^2/M2)^(1/2) assuming M1<M2. If M1 = M2, then that expression goes to 0 and there is no frequency gap, just acoustic modes like we would expect to see in a typical monoatomic lattice.