jaredennisclark wrote:I'm going to use the element carbon in my following examples -

It is my understanding that 12C and 13C are stable isotopes. 14C, however, is radioactive and unstable. So far so good, right?

My question is WHAT is it that makes 14C radioactive. WHY does the nucleus decay spontaneously, while the nuclei of 12C and 13C do not?

This may be a ridiculously simple answer, and if so, I apologize. A person has to learn sometime.

Rumraket wrote:What Arcanyn said is pretty much what I have been taught myself. Though, I was also taught that the "stabilizing" effect neutrons have on a nucleus is among others, also because their presence will increase the average distance between protons, relieving some of the stress of electromagnetic repulsion.

But I think this thread belongs in the physics section

Me over at RDF wrote:

Svartalf wrote:

newolder wrote:Where did all the gold on Earth come from? Let Neil deGrasse Tyson explain.

the article wrote:Gold is a rare, odd-numbered atom with 79 protons. Common atoms have an even number of protons.

I stumbled on this statement right at the start... any scientific validation that elements with odd atomic numbers are less common than those with even atomic numbers? with the likes of hydrogen, nitrogen, aluminium, phosphorus, chlorine or sodium all being odd numbered, that sounds like woo to me.

If my reading of nuclear shell theory is correct, I think what Neil deGrasse Tyson is referring to is the fact that certain combinations of protons and neutrons are more energetically favoured than others, and that even numbers of both tend to be the most energetically favoured, particularly once the total count exceeds around 40 nucleons. It's certainly unusual for a common element above, say, Zinc in the periodic table to have an odd count for both protons AND neutrons.

From a freely available textbook on radiochemistry:

3.1. Patterns of Nuclear Stability

There are approximately 275 different nuclei which have shown no evidence of radioactive decay and, hence, are said to be stable with respect to radioactive decay. When these nuclei are compared for their constituent nucleons, we find that approximately 60% of them have both an even number of protons and an even number of neutrons (even-even nuclei). The remaining 40% are about equally divided between those that have an even number of protons and an odd number of neutrons (even-odd nuclei) and those that have an odd number of protons and an even number of neutrons (odd-even nuclei). There are only 5 stable nuclei which are known to have both an odd number of protons and an odd number of neutrons (odd-odd nuclei); 2H1, 6Li3, 10B5, 14N7 and 50V23. It is significant that the first stable odd-odd nuclei are abundant in the very light elements (the low abundance of 2H1 has a special explanation: see Ch. 17). The last nuclide is found in low isotopic abundance (0.25%) and we cannot be certain that this nuclide is not unstable to radioactive decay with an extremely long half-life.

Considering this pattern for the stable nuclei, we can conclude that nuclear stability is favoured by even numbers of protons and neutrons. The validity of this statement can be confirmed further by considering for any particular element the number and types of stable isotopes: see Figure 3.1. Elements of even atomic number (i.e., even numbers of protons) are characterised by having a relatively sizeable number of stable isotopes, usually 3 or more. For example, the element tin, atomic number 50, has 10 stable isotopes while cadmium (Z=48) and tellurium (Z=52) each have 8. By contrast silver (Z=47) and antimony (Z=51) each only have 2 stable isotopes, and rhodium (Z=45), indium (Z=49) and iodine (Z=53) have only 1 stable isotope. Many other examples of the stabilisation of even numbers of nucleons can be found from a detailed examination of Figure 3.1, or easier, from the nuclide charts, e.g., Appendix C. The guide lines of N and Z equal to 2, 8, 20, etc., have not been selected arbitrarily. These proton and neutron numbers represent unusually stable proton and neutron configurations, as will be discussed further in Chapter 11. The curved line through the experimental points is calculated based upon the liquid drop model of the nucleus which is discussed later in this chapter.

Elements of odd Z have none, one or two stable isotopes, and their stable isotopes have an even number of neutrons, except for the 5 odd-odd nuclei mentioned above. This is in contrast to the range of stable isotopes of even Z, which includes nuclei of both even and odd N, although the former outnumber the latter. Tin (Z=50), for example, has 7 stable even-even isotopes and only 3 even-odd ones.

The greater number of stable nuclei with even numbers of protons and neutrons is explained in terms of the energy stabilisation gained by combination of like nucleons to form pairs, i.e., protons with protons and neutrons with neutrons, but not protons with neutrons. If a nucleus has, for example, an even number of protons, all of these protons can exist in pairs. However, if the nucleus has an odd number of protons, at least one of these protons must exist in an unpaired state. The increase in stability resulting from complete pairing in elements of even Z is responsible for their ability to accumulate a greater range of neutron numbers as illustrated in the isotopes of germanium (Ge32, 5 stable isotopes) relative to those of gallium (Ga31, 2 stable isotopes) and arsenic (As33, 1 stable isotope). The same pairing stabilisation holds true for neutrons so that an even-even nuclide which has all its nucleons, both protons and neutrons, paired represents a quite stable situation. In the elements in which the atomic number is even, if the neutron number is uneven, there is still some stability conferred through the proton-proton pairing. For elements of odd atomic number, unless there is stability due to an even neutron number (neutron-neutron pairing), the nuclei are radioactive with rare exceptions. We should also note that the number of stable nuclear species is approximately the same for even-odd and odd-even cases. The pairing of protons with protons and neutrons with neutrons must thus confer approximately equal degrees of stability.

Source for the above: Radiochemistry and Nuclear Chemistry, 3rd Edition Gregory Choppin, Jan Rydberg and Jan-Olov Liljenzin, ISBN 0-7506-7463-6. This book was, once upon a time, downloadable as separate chapters in PDF file format from here, but the site appears to be down at the moment (sigh).

This makes sense if you realise that protons and neutrons are fermions, which means that they are particles that obey Fermi-Dirac quantum statistics, and that the Pauli Exclusion Principle applies to them. This means that in any given quantum system, no two particles can share the exact same quantum numbers. In the case of electrons, this is already well known, and leads to the appearance of electron shells organised according to the quantum numbers that electrons occupy. A similar situation occurs with protons and neutrons, in that two nucleons sharing a set of non-spin quantum numbers, but with opposite spins, can pair up, analogous to the manner in which electrons pair up, but because the details of the quantum numbers for nucleons are rather more complicated, the nuclear shell model for nucleons is correspondingly more complex than the electron shell model.

Taking a look at a typical table of nuclides (Kaye & Laby supply a complete one here), and looking at the entry for gold, there is only one stable isotope: 197Au79, with 79 protons and 118 neutrons. All the other isotopes are unstable. Compare with nearby platinum (Z=78), which has the following stable (or extremely long lived) isotopes:

190Pt - 0.01% natural abundance, half life 6.5 × 1011 Yr
192Pt - 0.79% natural abundance, stable
194Pt - 32.9% natural abundance, stable
196Pt - 33.8% natural abundance, stable
198Pt - 7.2% natural abundance, stable

or for that matter mercury (Z=80), which has the following list of stable/long-lived isotopes:

196Hg - 0.15% natural abundance, stable
198Hg - 9.97% natural abundance, stable
200Hg - 23.10% natural abundance, stable
202Hg - 29.86% natural abundance, stable
204Hg - 6.87% natural abundance, stable

Incidentally, with respect to the oddball (i.e., the unusually heavy odd-odd) isotope 50V mentioned in that textbook, which the textbook states may be radioactive, this has since been determined to be the case. 50V is very slightly radioactive, and has a half life of 1.5 × 1017 years, so that for practical purposes during any given human lifetime, it can be treated as a stable element, because in any sample other than a very large sample of this isotope, you would be lucky to detect one atom decaying in a typical human lifetime. Another extremely long-lived radionuclide is 209Bi, which was suspected to be radioactive for a long time, but whose radioactivity had never been directly observed. This has now been observed by a French laboratory, and the half-life of 209Bi is a whopping 1.9 × 1019 years.

Actually, the "island of stability" centres upon atomic number 114, not 122. There are reasons for this, namely the fact that specific numbers of nucleons in a nucleus are especially stable. This is a consequence of the nuclear shell model, which posits that nucleons occupy energy levels in a nucleus in the same manner that electrons do, as a direct consequence of the fact that protons and neutrons are fermions (particles with half-integer spin angular momentum quantum numbers) and therefore obey Fermi-Dirac statistics and in particular the Pauli Exclusion Principle. The numbers of nucleons that can occupy a particular shell is determined by the number of nucleons that can possess unique values of the various quantum numbers associated with a given energy level (which in turn is associated with the principal quantum number n). the actual quantum numbers that are used in the nuclear shell model differ from those used for election orbits because the spin-orbit interaction has to be taken into account much more rigorously - in electron orbits, this gives rise to level splitting that can be observed in spectra, but electrons move relatively freely, while nucleons do not (their motion is much more constrained). So, the quantum numbers that are used are:

n - Principal quantum number (0, 1, 2, ....)

j - Total Angular Momentum quantum number (1/2, 3/2, ... n-1/2 for any given n)

mj - projection of j along a specific axis (-j, -j+1, ... +j) for any given j

p - Parity. To define parity, we need to construct another quantum number, namely the Azimuthal Quantum Number l. l is set to take values from 0 to n-1 for any given n. If n is even for a given state, then the parity is even (+), else it is odd (-).

For n=0, this gives the following possible states:

n=0, j=1/2, mj=-1/2, l=0(+)
n=0, j=1/2, mj=+1/2, l=0(+)

Therefore the lowest shell can only contain two nucleons.

The next shell is n=1. The possible states that can be occupied are:

n=1, j=1/2, mj=-1/2, l=1(-)
n=1, j=1/2, mj=+1/2, l=1(-)
n=1, j=3/2, mj=-3/2, l=1(-)
n=1, j=3/2, mj=-1/2, l=1(-)
n=1, j=3/2, mj=+1/2, l=1(-)
n=1, j=3/2, mj=+3/2, l=1(-)

This is 6 states, so that the total number of nucleons that can exist in this level is 6, and the total number of nucleons that can exist in all available energy levels is 2+6=8 when all energy levels are completely filled.

For n=2, we have:

n=2, j=1/2, mj=-1/2, l=2(+)
n=2, j=1/2, mj=+1/2, l=2(+)
n=2, j=3/2, mj=-3/2, l=2(+)
n=2, j=3/2, mj=-1/2, l=2(+)
n=2, j=3/2, mj=+1/2, l=2(+)
n=2, j=3/2, mj=+3/2, l=2(+)
n=2, j=5/2, mj=-5/2, l=2(+)
n=2, j=5/2, mj=-3/2, l=2(+)
n=2, j=5/2, mj=-1/2, l=2(+)
n=2, j=5/2, mj=+1/2, l=2(+)
n=2, j=5/2, mj=+3/2, l=2(+)
n=2, j=5/2, mj=+5/2, l=2(+)

Therefore there are 12 states in the n=2 energy level. Therefore there can be 12 nucleons in this energy level, and there can be 2+8+12=20 nucleons in all energy levels up to n=2 if all energy levels are filled.

Things get a bit more complicated for n=3 and beyond, as those energy levels are subject to additional interactions that require the elimination of some states that conflict with existing states (for intricate quantum mechanical reasons that start to make my head hurt at this stage, let alone anyone else's), but as a consequence of all this, the possible numbers of nucleons that exist for all filled energy states is as follows:

2, 8, 20, 28, 50, 82, 126, 184 ...

These numbers correspond to nuclei with especially stable configurations of nucleons (protons and neutrons), but not all species actually exist. He2 is unknown, but He4 is the familiar Helium isotope and is extremely stable. O8 is unknown, as is O10, but O16 is the familiar Oxygen isotope and is extremely stable. Likewise, the stablest isotope of Calcium is Ca40 (20 protons, 20 neutrons). For the heavier elements, other considerations start to make themselves felt, such as the need for increasing neutron richness to enhance stability as the proton number grows, so the next stable element, Nickel, actually has an unstable isotope Ni56 and the first stable isotope is actually Ni58. Likewise, the first stable isotope of Tin is Sn112 instead of Sn100 (which is not yet even known to exist). By the time we reach Lead, the stablest isotope is actually Pb208 (82 protons, 126 neutrons, both 'magic numbers'.) Incidentally, with respect to Nickel, even here the greatest stability is found not in a Nickel isotope, but in Fe56 (the end of the road for nucelosynthesis in massive stars and the accumulation of which during highly unstable Si fusion leads to a supernova).

Once we reach the Transuranic elements, things get seriously complicated, because spontaneous fission looms on the horizon, which is why the elements from about atomic number 105 onwards are ever more difficult to synthesise, and their half-lives start to plummet dramatically to milliseconds or even shorter durations, which means that to synthesise them and detect them requires great effort. Their actual chemistry will only be predicted, never observed, because they will not last long enough to form chemical compounds that can be analysed, unless someone comes up with a clever means of observing chemical reactions in a particle accelerator.

Now, the next 'magic number' in the list is 126. The problem here is that this business of spontaneous fission pulls the next stable number of protons down from 126 to 114. This is the "island of stability" that was targeted by the Joint Institute for Nuclear Research in Dubna, Russia, and Otyonkov and Oganessian published an article in which they claimed to have synthesised just one atom of element 114 (after running their apparatus for 40 days solid!) by performing a specialised nuclear fusion of two exotic neutron-rich isotopes, Pu244 and Ca48, which had to be manufactured in situ as they are both unstable, and had to be reacted together in the beam chamber. The reason for choosing these isotopes was that the resulting excited nucleus, E114178, would not fission, as the evaporation of three neutrons to form E114175 would remove sufficient energy from the resulting nucleus to take it below the fission threshold. Now, Utyankov and Oganessian's original work was hotly disputed, and other workers in places such as Darmstadt have synthesised other elements including Hassium-270 (Hs270), which is atomic number 108, this synthesis being performed in 2006 (news article here).

Part of the problem with the nuclear shell model is that it was originally constructed with the idea of all stable nuclei being spherical. This is no longer considered to be the case, and various deviations from sphericity are now considered to be stable for heavier elements, hence the deviations from the correlation between stability and strict adherence to the 'magic number' sequence. To understand why this is the case, one is required to spend a good four or five years studying nuclear physics at Masters level, and since my command of the intricacies of nuclear physics do not extend quite to that level, I shall have to hand over at this point to someone more qualified.

So, any claims that there exists a sufficiently stable isotope of element 122 will require an extraordinary degree of evidential confirmation, given the difficulties that scientists have experienced reaching element 114, which is calculated to be considerably more stable than element 122.