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)?
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.