My (extremely limited) understanding of what causes an element to be either stable or reactive is due to a mismatch in energy in the nucleus due to either extra protons or extra neutrons. So why wouldn’t something like Plutonium-188 be stable, since it would have 94 protons and 94 neutrons?
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>So why wouldn’t something like Plutonium-188 be stable, since it would have 94 protons and 94 neutrons?
Firstly, There are no stable elements heavier than lead (Z=82)
This is because the strong nuclear force, has a quite short range of influence, while electrical repulsion of protons has infinite range. Therefore the larger a nucleus becomes, the less strongly one given proton is restrained against it’s mutual electrical repulsion against all other protons in the nucleus. Therefore for elements heavier than lead, you see either alpha decay (emission of a helium atom), or spontaneous fission in the case of elements heavier than uranium.
Alpha particle emission is the result of the process of quantum tunneling. It may be seen in a certain sense as a type of nuclear fission.
Secondly, The heaviest element with a stable isotope with a 1:1 ratio of z/N is element 20, calcium. Specifically the isotope calcium 40. (n being the number of neutrons and Z being the atomic number on the periodic table.)
For all heavier elements than calcium, rhe stable isotopes are always *Neutron Rich.* moreover the heavier the element is, the greater the average n/Z ratio becomes.
The only two stable proton-rich isotopes are helium-3 and hydrogen-1. H-1 being a trivial case.
This is related to the isotope Ca-20 being “doubly magic” meaning it has a magic number of both protons and neutrons. Magic numbers are analogous to the noble gasses, in the realm of electron structure. Noble gasses have completely filled electron shells causing the electrons to be in a particularly low energy state and therefore be very unreactive.
With calcium having a magic N (atomic number) it also has an unusually large number of stable isotopes (4) compared to K and Scandium. both of those have only one stable isotope. Sc-46 is just barely stable and has a strong tendency to absorb neutrons, after which it quickly decays into titanium-46 which is far more common in the earth’s crust than Scandium. In large stars, any scandium that is produced tends to be converted into titanium. So it has low abundance. This is why calcium and titanium are common in the universe at large but potassium is significantly rarer and scandium is much rarer.
Likewise isotopes that have magic numbers of either protons or neutrons are exceptionally stable because the nucleus is at a lower energy state by comparison to nearby isotopes or elements with similar neutron numbers.
Lead is another example of a magic numbered nucleus (Z=82) as such, it’s unusual in having four stable isotopes despite how heavy it is, compared to bismuth (one isotope that’s slightly unstable) and thallium (one stable and one that’s theoretically unstable but it’s decay hasn’t been observed reliably)
Therfore, it’s almost certainly impossible that Pu-188 could be formed for any length of time, however brief. There is simply not nearly enough strong interaction force to hold such a nucleus together at all without about 50 more intervening neutrons. Likewise, the isotope silver-94 (47n/47Z) itself only has a half life of about 27 milliseconds. So it decays almost instantly after being formed. Therefore you couldn’t use a particle accelerator to form Pu-188 by fusing 2 Ag-94.
>So why wouldn’t something like Plutonium-188 be stable, since it would have 94 protons and 94 neutrons?
Firstly, There are no stable elements heavier than lead (Z=82)
This is because the strong nuclear force, has a quite short range of influence, while electrical repulsion of protons has infinite range. Therefore the larger a nucleus becomes, the less strongly one given proton is restrained against it’s mutual electrical repulsion against all other protons in the nucleus. Therefore for elements heavier than lead, you see either alpha decay (emission of a helium atom), or spontaneous fission in the case of elements heavier than uranium.
Alpha particle emission is the result of the process of quantum tunneling. It may be seen in a certain sense as a type of nuclear fission.
Secondly, The heaviest element with a stable isotope with a 1:1 ratio of z/N is element 20, calcium. Specifically the isotope calcium 40. (n being the number of neutrons and Z being the atomic number on the periodic table.)
For all heavier elements than calcium, rhe stable isotopes are always *Neutron Rich.* moreover the heavier the element is, the greater the average n/Z ratio becomes.
The only two stable proton-rich isotopes are helium-3 and hydrogen-1. H-1 being a trivial case.
This is related to the isotope Ca-20 being “doubly magic” meaning it has a magic number of both protons and neutrons. Magic numbers are analogous to the noble gasses, in the realm of electron structure. Noble gasses have completely filled electron shells causing the electrons to be in a particularly low energy state and therefore be very unreactive.
With calcium having a magic N (atomic number) it also has an unusually large number of stable isotopes (4) compared to K and Scandium. both of those have only one stable isotope. Sc-46 is just barely stable and has a strong tendency to absorb neutrons, after which it quickly decays into titanium-46 which is far more common in the earth’s crust than Scandium. In large stars, any scandium that is produced tends to be converted into titanium. So it has low abundance. This is why calcium and titanium are common in the universe at large but potassium is significantly rarer and scandium is much rarer.
Likewise isotopes that have magic numbers of either protons or neutrons are exceptionally stable because the nucleus is at a lower energy state by comparison to nearby isotopes or elements with similar neutron numbers.
Lead is another example of a magic numbered nucleus (Z=82) as such, it’s unusual in having four stable isotopes despite how heavy it is, compared to bismuth (one isotope that’s slightly unstable) and thallium (one stable and one that’s theoretically unstable but it’s decay hasn’t been observed reliably)
Therfore, it’s almost certainly impossible that Pu-188 could be formed for any length of time, however brief. There is simply not nearly enough strong interaction force to hold such a nucleus together at all without about 50 more intervening neutrons. Likewise, the isotope silver-94 (47n/47Z) itself only has a half life of about 27 milliseconds. So it decays almost instantly after being formed. Therefore you couldn’t use a particle accelerator to form Pu-188 by fusing 2 Ag-94.
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