Caesium-133 is stable. Caesium-134 and caesium-137 are radioactive isotopes of caesium with half-lives of 2.065 years and 30.17 years respectively.
Why does caesium-137 have a longer half-life if it contains three more neutrons than caesium-134 and four more neutrons than stable caesium?
It would seem to me that caesium-134 would have the longer half-life given that it only contains one more neutron than stable caesium.
Answer
As noted in the comments, all of the various Cs isotopes I'll mention decay by emitting a beta, converting the Cs isotope to a Ba isotope. Now, while details of nuclear decays are not necessarily touched on unless you are in a nuclear physics course, they are at least somewhat analogous to electron or photon decays. What I mean by that is that you are, at a hand-waving level, looking at an initial state (the Cs), final states (Ba in various possible energy levels), and any applicable quantum numbers you would like to try and conserve (like nuclear spin).
So, lets take a tour of the isotopes, relying mainly on data from nuclear data sheets. Start with Cs-134 (you probably did not know there was a journal called Nuclear Data Sheets). Going down to page 69, one finds that the Cs-134 nucleus has a spin of 4. It can decay to any one of 6 possible Ba-134 nuclear energy levels (the ground state and 5 excited states). The majority of the decays go through an excited state, which also has a nuclear spin of 4. The half life is 2 years.
Cs-135 is listed with a nuclear spin of 7/2. There is only one available Ba-135 level to decay to, and it has a nuclear spin of 3/2. The half life of this decay is 2.3 million years. Only one state to go to, and a spin mismatch to slow it down.
Cs-137 has a nuclear spin of 7/2. It can decay in to 3 different Ba-137 levels, the ground state and two excited states. The majority go through an excited state with spin 11/2. The other two states have spin 1/2 or 3/2 (the ground state). So, a few more states to decay to, but some pretty large spin mismatches on several of them. The half life is 30 years.
Cs-139 has a nuclear spin of 7/2. It can decay in to one of 60 (!) different Ba levels, with most decays being to the ground state which has a spin of 7/2. The half life is 9 minutes.
Taken all together, what do we see?
More available levels to decay to increases the chance of decaying. Closer spin values between the parent and daughter nuclei increases the chance of decaying. To go much deeper requires diving deeper in to nuclear physics.
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