[Chemistry] When are isotopes radioactive?
Good day,
I still need a little help to identify when isotopes are radioactive. I'm really looking forward to your helpful and detailed answers.
C-14 is radioactive, which means that fossils can be dated using their half-life, a process known as radiocarbon dating.
But why is the isotope C-14 radioactive? C-14 has 6 protons and 8 neutrons. Is there a general rule for determining when an isotope is radioactive?
I thought it might be due to the number of protons and neutrons. Perhaps it always happens when the number of protons and neutrons is unequal. But that doesn't seem to be the case, because I found the following on the internet:
Carbon-13 has 6 protons and 7 neutrons. But carbon-13 is apparently not radioactive. So how can you tell whether an isotope is radioactive or not?
(2 votes)
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Unfortunately, not at all. It's quite complex, and there's no simple rule.
If the atom is energetically stable, then it is stable. Whether an atom is stable or not can't be determined by looking at it or laying on its hands (unless it's completely escalated); it has to be calculated.
You can use the Bethe-Weizsäcker formula (which works quite well for most atoms) as an approximation. It's pretty simple; you just need to plug in. Copied here from Wikipedia:
Calculating it to half an equatorial degree, however, is not trivial and cannot be done casually.
Using the Bethe-Weizsäcker formula, you can approximately calculate the mass of an atom/nucleus and thus the binding energy, but by inserting it alone you cannot find out whether a nucleus is stable (the fact that the binding energy is positive is not enough).
I said approximately. If the binding energy is n't positive, you already know that the nucleus is n't stable. And if the binding energy is very high , you can assume with a high degree of probability that the nucleus is stable.
I thought I'd made it abundantly clear that this is only a rough approximation or an indication, and not an exact calculation. But okay, just point it out again…
In principle, that's true. Nuclei with a balanced proton-neutron ratio are stable; heavier nuclei with a slight neutron surplus are stable due to the increasing repulsion between the protons. Alpha decay, however, also comes into play, which becomes energetically worthwhile above a certain gravity (mass number approximately 170). The greater the distance from stability, the more likely radioactivity is. Carbon-13 just barely passes through. In the case of tin, even 10 stable isotopes pass through. A few other factors also play a role in stability: the surface-to-volume ratio of the nucleus, the even or odd number of protons and neutrons ("pairing possibility"), their respective total number ("magic numbers" = particularly stable), and so on.
Why things are radioactive is a very complex topic in quantum physics. If you're interested, I know a video that explains it all very well.
https://www.youtube.com/watch?v=mqgmKzRneic
In general, you can always look at a radionuclide chart, which is something like an extended periodic table that also includes all the isotopes of the elements, to see which isotopes are radioactive and which are not.
For this purpose, one uses the Karlsruhe Nuclide Map, for example. It shows which isotopes decay and how.
I don't know that the ratio between protons and neutrons can be used to reliably determine whether an isotope is radioactive.