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How can we predict which particle the radioactive element will emit?

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  • $\begingroup$ Are you asking which decay channel an isotope with multiple possible decays will take and when the decay will take place? That's unpredictable. Or are you asking how we can predict the possible decay channels? $\endgroup$
    – CuriousOne
    Dec 25, 2014 at 13:47
  • $\begingroup$ I am just asking that how will we know whether the emission that is going to happen is alpha,beta or gamma? $\endgroup$ Dec 25, 2014 at 13:49
  • $\begingroup$ I can take a guess... my nuclear physics is very rusty. The primary driver for decays is nuclear binding energy. A radioactive isotope has to be in a higher energetic state than the sum of its decay products. Possible decays channels are to lower Z by alpha decay (Z->Z-2), by conversion of a proton to a neutron (Z->Z-1), to the same Z by emission of a gamma or to higher Z by conversion of a neutron to a proton (electron capture). The higher the energy difference between the initial and the final state, the more likely the process. The details are greatly complicated by nuclear structure. $\endgroup$
    – CuriousOne
    Dec 25, 2014 at 14:01
  • $\begingroup$ Processes with shorter half-life are more likely to occur. $\endgroup$
    – Sofia
    Dec 25, 2014 at 15:02
  • $\begingroup$ You get alphas from very heavy nucleii (e.g., actinides). The daughter nucleus then often has an excess of neutrons. Nucleii with an excess of neutrons tend to beta- decay. Other, more esoteric decay modes tend not to occur in nature, but can happen in nucleii that have been transmuted in a reactor or in a particle accelerator. Gamma emission often follows immediately or soon after other types of decay which usually leave a nucleus in a high-energy state. $\endgroup$ Jan 7, 2016 at 21:57

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An unstable nucleus may have a set of possibilities of decay channels, as you say, alpha decay, beta decay, neutron(s) emission, proton emission, gamma rays. A nucleus with deficit of protons is likely to emit positrons. A nucleus too much rich in neutrons may undergo beta decay.

Now all these possibilities compete, however, the most likely to be chosen is the channel with the shortest half-life. (See also the information in the comments below.)

Still, this is statistics, it can be applied for a sample of many nuclei.

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  • $\begingroup$ Are you aware of simple rules of thumb in nuclear physics to estimate the decay channels and half lives? My last nuclear physics class was decades ago and I never had to look at that question since. $\endgroup$
    – CuriousOne
    Dec 25, 2014 at 15:21
  • $\begingroup$ I am currently dealing with the decay. Half-lives have to be calculated and the calculus is according to very complicated formulas, and these formulas are provided by nuclear models as liquid drop model, cluster model, shell model and others. $\endgroup$
    – Sofia
    Dec 25, 2014 at 19:19
  • $\begingroup$ Thanks! I figured that there is no easy way that gets around the structure calculations. $\endgroup$
    – CuriousOne
    Dec 25, 2014 at 20:13
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    $\begingroup$ Please see: none of the models is perfect. A good book on the decay is that of my advisor, Doru Delion, "Theory of Particle and Cluster Emission". It's hundreds of pages of theory. For instance in the alpha decay there is a competition between two processes, the alpha formation (more exactly construction) from its nucleons, and the emission. Now, prof. G. Royer prefers to work with the liquid drop model. The truth is probably somewhere in between all the models. Anyway there are different formulas for $T_{1/2}$ for even-even nuclei, for odd-odd, odd-even and even-odd. Indeed, it's not simple. $\endgroup$
    – Sofia
    Dec 25, 2014 at 20:29

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