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I am guessing that isotopes with an even number of neutrons more readily release an alpha particle... When and if At-210 does that, it still has the problem of being 'odd/odd'...

But this begs the question... Why can't highly unstable isotopes like this just emit a neutron? Rather than 'waiting' for beta decay (or electron capture) to occur?

Why isn't the radioactive emission of a single neutron or proton, via quantum tunneling perhaps, as common as alpha decay (via quantum tunneling)?

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Leaving aside the questions of why only certain decay options are observed, lets just compare the known decays of At-210 and your proposed neutron emission.

Going to the latest Atomic Mass Evaluation (2020 version, part II with the tables of masses) one can look up the masses of various nuclei as well as their decay products. One finds:

Nuclei Mass (amu) Delta (amu)
At-210 208.986169 0
At-209 + n 209.9948339 +0.007686
Po-210 (ec) 209.9828737 -0.004273
Bi-206 + $\alpha$ 209.9811023 -0.006044

The deltas show that At-210 cannot decay to At-209 plus a neutron - the total mass of the products increases, meaning it is not energetically possible. The other decay paths are exothermic. Further, the alpha decay is more energetically favorable, that is the total mass after alpha decay is less than for beta decay.

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