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Why do U and Th (and Pu) have so long half lives in comparison with the lighter elements following Bi (i.e. Po, Ra, Rn, Fr, At ..)?
Bill_K said:(This is an interesting point. In the popular mind, Uranium is "highly radioactive". When in fact it is hardly radioactive at all!)
Because Uranium has a low disintegration energy, and the escaping alpha particle has a Coulomb barrier through which it must tunnel. The systematic variation of half-life with disintegration energy is known as the Geiger-Nuttall rule.
Bill_K said:Q is the disintegration energy, and while the values plotted are experimental data, he also obtains rough agreement from the semiempirical mass formula. For example the formula predicts Q > 0 for heavy nuclei, and a slight trend of decreasing Q for increasing A, constant Z.
Yes, the instabilitly of Polonium etc. is clear. Nevertheless I don't understand why stability rises again for Th and U in a region which is far away from magic numbers.bcrowell said:I think you do need to invoke shell effects for a full explanation. Otherwise it's hard to imagine any explanation for the oscillating off-on-off-on pattern of alpha decay as you go up in Z from lead. If shell effects were not present, then you would only have liquid-drop physics, and there would only be two effects: (1) a Q value that smoothly increased with Z, and (2) a Coulomb barrier that changed smoothly with Z. I don't see how two such smooth effects could lead to the observed oscillation.
I could be wrong, but I think what's going on is this. The smooth trend is that due to liquid-drop physics, Q values for alpha decay increase smoothly as you go up in Z. Superimposed on top of this, you have some shell effects that become decisive for a few isotopes near the border between alpha-stability and alpha-instability. Lead is stable because of shell effects (magic number 82), so it doesn't alpha decay (Q<0). Stuff a little above lead, such as polonium, can get closer to magic number 82 by alpha decaying, so you get Q>0.
See also: http://en.wikipedia.org/wiki/Island_of_stability
Bill_K said:Suit yourself, DrDu, but I have already given you the reason - it comes from the semiempirical mass formula.
DrDu said:Yes, the instabilitly of Polonium etc. is clear. Nevertheless I don't understand why stability rises again for Th and U in a region which is far away from magic numbers.
You're speaking as though shell effects and Q values were separate considerations. They're not. Part of what determines the Q values is shell effects. I really don't see how you can explain an oscillatory effect based on a "slow steady variation."Bill_K said:Suit yourself, DrDu, but I have already given you the reason - it comes from the semiempirical mass formula. Thanks to the amplifying effect of the Coulomb barrier, it only takes a small difference in Q to make an enormous difference in the half-life. I'm not talking about the pairing term, and I'm not talking about shells, although they have an effect too. It's the slow steady variation caused by the volume and surface terms in the mass formula.
I don't think anyone has suggested that only Z matters. It's just that the instability of heavy elements is driven by the Coulomb repulsion, so Z is an important factor in the macroscopic part of the binding energy. If you look at the Moller-Nix figure, it looks like we can make sense out of the thorium data. As you go from 228Th to 230Th (N=138 to N=140), it looks like the shell correction is flattening out, which would tend to make the Q value lower for 230Th.Bill_K said:And it is not just, as you seem to think, a trend between different elements. It is not just that heavy elements are longer lived than light ones. It is also an isotope effect. Compare the alpha half-lives for the isotopes of one element, Thorium say,
Th-228 is 1.91 y
Th-229 is 7300 y
Th-230 is 75,400 y
An example of what I'm talking about is the plot of Qα on page four of this. Naturally the shell effect is quite noticeable - near the shell boundaries (N = 126 and Z = 82). But overall the variation is slow and smooth. Pick any Z value and follow the curve - it's slanted downward as A increases, at a nearly steady slope. For the transuranics there's a general upward tendency, but below that, Qα is remarkably flat. Yes, there's a barely perceptible odd-even staggering, but I don't really see any "oscillatory effect".You're speaking as though shell effects and Q values were separate considerations. They're not. Part of what determines the Q values is shell effects. I really don't see how you can explain an oscillatory effect based on a "slow steady variation."
DrDu said:Why do U and Th (and Pu) have so long half lives in comparison with the lighter elements following Bi (i.e. Po, Ra, Rn, Fr, At ..)?
Bill_K said:Yes, there's a barely perceptible odd-even staggering, but I don't really see any "oscillatory effect".
I'm baffled by your characterization of that graph. It's entirely dominated by large up-down oscillations caused by shell effects. It is not true, as you seem to be claiming, that the trend is monotonic for fixed Z. For example, take another look at the bismuth isotopes, which are highlighted in red. The red curve goes high-low-high-low. The most prominent feature is a sharp minimum at A=209, which corresponds the magic neutron number 126.Bill_K said:An example of what I'm talking about is the plot of Qα on page four of this. Naturally the shell effect is quite noticeable - near the shell boundaries (N = 126 and Z = 82). But overall the variation is slow and smooth. Pick any Z value and follow the curve - it's slanted downward as A increases, at a nearly steady slope. For the transuranics there's a general upward tendency, but below that, Qα is remarkably flat. Yes, there's a barely perceptible odd-even staggering, but I don't really see any "oscillatory effect".
Bill_K said:An example of what I'm talking about is the plot of Qα on page four of this.
Uranium (U) and Thorium (Th) have long half lives because they are both radioactive elements, meaning they emit radiation as they decay. The longer the half life, the slower the rate of decay, which allows for these elements to exist in the Earth's crust for millions of years.
The half life of U and Th can be determined through a process called radiometric dating. This involves measuring the amount of a radioactive element and its decay products in a sample, and using this information to calculate the half life of the element.
U and Th half lives have many practical applications, including dating the age of rocks and minerals, studying the Earth's history, and determining the age of artifacts. They are also used in nuclear power plants to generate electricity.
No, the half lives of U and Th are constant and do not change. This is a fundamental property of radioactive elements and is not affected by external factors such as temperature or pressure.
Yes, there are other elements with longer half lives than U and Th. For example, bismuth-209 has a half life of over 1 billion years, making it the longest-lived naturally occurring element. However, U and Th still have some of the longest half lives among commonly found radioactive elements.