Do all isotopes have a half life? I understand that some isotopes of an element have a shorter half life, and decay more quickly into other elements. Other isotopes are described as stable and no half life is stated. For elements that have a stable isotope, does this isotope still have a half life, just a very long one? Are there isotopes which do not decay spontaneously, or do all isotopes have a half life?
 A: This given link is list of different isotopes with half life time
http://en.wikipedia.org/wiki/List_of_radioactive_isotopes_by_half-life
The release of radiation by unstable nuclei is called radioactive decay. This process occurs naturally and cannot be influenced by chemical or physical processes. The release of radiation is also a random event and overtime the activity of the radioactive material decreases. It is not possible to predict when an individual nucleus in a radioactive material will decay. But it is possible to measure the time taken for half of the nuclei in a radioactive material to decay. This is called the half life of radioactive material or radioisotope.
This is the latest list of known isotopes :
http://periodictable.com/Properties/A/KnownIsotopes.html
given link below is I trust more 
http://ie.lbl.gov/education/isotopes.htm
A: Please see, like an atom that has a ground state, and in that state it would remain always if it not disturbed by some influence from outside, (some irradiation with other particles), so there are nuclei whose state is the ground state. Such nuclei have no excess of energy to get rid of.
Let me give some examples: there are nuclei with too many protons, s.t. teir configuration is unstable. They are likely to undergo $\beta ^+$ decay, and emit a positron. Other nuclei have to many neutrons, s.t. they may emit one or more neutrons, or may undergo $\beta ^-$ decay.
In short, yes, there are stable nuclei, or, in other words, there are ground states for nuclei. 
Long lived unstable isotopes, are not in the ground states, but in some resonant states, very narrow from the point of view of the energy range encompassed by that resonance. The narrower the resonance, the longer is its half-life. But, I repeat, a resonant state, long lived as it may be, is not a ground state.
