Radioactivity.

1) Am I correct in thinking that radioactivty can basically be classified into two types :
i)an unstable nucleus (dictated by the ratio of proton number to nucleon number)
ii) an excited atom - occupying an energy level other than its ground.

and so in the above case, the first decay is an example of an unstable nucleus decaying into a more stable nucleus(situation i), whereas the second case is simply a result of the barium 137 being fromed in an excited state and thus can only ocupy this state for a limited amount of time - the transiition occuring via emission of a gamma ray(situation ii).

2) So also, that i includes beta and alpha radation only (and not gamma) whereas ii includes only gamma photons (and not beta and alpha).

3) Also in case ii) if one is to measure the half-life of Ba-137m are you basically measuring the lifetime of its metastable energy state?

Many Thanks for any assistance !

Not quite. Nuclear (in)stability is not dictated solely by neutron to proton ratio. The transformation of an unstable nucleus to a more stable configuration is achieved by radioactive decay, generally by alpha or one of the three types of beta decay.

That transformation may be accompanied by the generation of a product nucleus in an excited state and, when that de-excites, gamma ray photons are emitted.

It is better to look at radioactive decay as being the transformation of a nucleus to a more stable one, which may be accompanied by a range of different processes.

In answer to your Q3, yes- the half life of the isomer is indeed a measure of its lifetime

Does this imply that only one n value is occupied by the Ba-137m , that only one value is metastable, otherwsie the time to de-excite would surely vary with n?(or I have interpreted the definition of life-time incorrectly).

What do you mean by 'only one n value'?