Are stable atoms stable?

[Tubbythin]

For purposes of nuclear decay, I'd call anything lighter than iron "light", and anything heavier than iron "heavy". Roughly speaking, of course. The reason is that iron has the lowest energy (per nucleon) of any atom:

http://en.wikipedia.org/wiki/Binding_energy#Nuclear_binding_energy_curve

Actually, Nickel-62 has the greatest (negative) binding energy per nucleon. It just can't be made in normal stellar environments. Hence the peak in abundances is at iron-56.

 

[Ziggurat]

What would you call iron?

Just right.

 

[jasonpatterson]

Roughly speaking, one gram of anything contains 6x10^23 nucleons. For something with a half-life of T, you will see 6x10^23 decays per gram per T.

I thought this was all well done except for the second number. If the half-life is T, then HALF of the sample decays in that time. So if you start with 1 gram, you'd expect to see 3x10^23 decays in T. This also assumes that there is no additional stability that occurs by virtue of the nucleon existing in a nucleus, as is observed in a neutron. You'd need 1g of hydrogen-1 for this to be the case.

The big problem with observing these rarely seen phenomena is background noise. If I have a chunk of bismuth, it is likely contaminated with other elements that are radioactive as well as isotopes of bismuth that are not Bi-209 (that are more radioactive.) To record a decay event, I'd need to identify it as such because its energy was unexplainable by any other reasonable decay. The problem of detecting a proton decay is even greater, because of the insanely long lower limits to its half life (10^31 years as a lower limit, as mentioned.) You'd need to watch 87,400 metric tons of hydrogen to observe an average of 1 decay per day if this lower limit was the actual half life, assuming that detection was 100% accurate.

 

[MattusMaximus]

What would you call iron?

(I'm guessing that you'd class it as the heaviest light element.)

Iron is at the top of the nuclear binding energy curve...

http://en.wikipedia.org/wiki/File:Binding_energy_curve_-_common_isotopes.svg

If I interpret that curve correctly, I believe this makes Fe-56 the most stable nucleus.

Actually, Nickel-62 has the greatest (negative) binding energy per nucleon. It just can't be made in normal stellar environments. Hence the peak in abundances is at iron-56.

Ah yes. Good point of clarification.

 

[ben m]

I thought this was all well done except for the second number. If the half-life is T, then HALF of the sample decays in that time. So if you start with 1 gram, you'd expect to see 3x10^23 decays in T. This also assumes that there is no additional stability that occurs by virtue of the nucleon existing in a nucleus, as is observed in a neutron. You'd need 1g of hydrogen-1 for this to be the case.

On the first point: yeah, that was meant to be an order-of-magnitude calculation. 2 = sqrt(2) = 1 and all that. On the second point: you're right, and experiments are always careful to quote separate measurements of "proton lifetime" and "nucleon lifetime in 16O nucleus" and so on.

The problem of detecting a proton decay is even greater, because of the insanely long lower limits to its half life (10^31 years as a lower limit, as mentioned.) You'd need to watch 87,400 metric tons of hydrogen to observe an average of 1 decay per day if this lower limit was the actual half life, assuming that detection was 100% accurate.

The proton problem is quite different than the bismuth one. 209Bi decays to a 3.1 MeV alpha particle, which, unless your detector is clever, looks a lot like any other 3 MeV decay or Compton scatter or whatever. Proton decay looks nothing like any nuclear event: it will be a multi-100 MeV event involving pions or hard leptons, whereas all nuclear events are in the sub-10-MeV ballpark. Cosmic-ray muons and atmospheric neutrinos (!) are possible backgrounds, but radioactivity is not.

 

[SezMe]

I'm 54.
I'm getting the impression from this thread that I can count on most of the universe not decaying before I'm dead?

Indeed yes. But at a very minor planet called Earth, there is far more decay than you would probably want.

 

[jasonpatterson]

The proton problem is quite different than the bismuth one.

Agreed, I should have broken that into two paragraphs. I was intending to say that the slow rate of decay was the biggest problem with actually detecting a proton decay (if such a thing ever even happens.) You have to watch an immense quantity of stuff for a long time before you can expect (statistically speaking) to see one decay.