How Can We Measure the Decay Rate of Uranium-238 Given Its Long Half-Life?

[dmehling]

I have a really basic question about radioactive decay. If it takes 4.4 billion years for uranium-238 to decay into thorium-234, how can the decay rate be measured? What intermediate activity is taking place that would give an indication of the time it would take an atom to decay into the next element in the decay chain?

 

[nasu]

You can measure the decay rate of a known amount of the isotope.
From this you can calculate the half-life time.

 

[Drakkith]

The key you're missing is that the half-life of u-238 is 4.4 billion years. This means that each atom of u-238 has a 50% chance of decaying to thorium-234 after 4.4 billion years has elapsed. So if we have a block of u-238, then after 4.4 billion years approximately half of the u-238 will have decayed. Then after another 4.4 billion years approximately half of the remaining u-238 will have decayed.

Make sense?

 

[dmehling]

I understand how the half-life works. I don't understand how it could be determined that it takes 4.4 billion years. We obviously can't measure something that takes that long. So how is it done? How do we know it takes 4.4 billion years. I'm obviously missing some important step.

 

[Nugatory]

I have a really basic question about radioactive decay. If it takes 4.4 billion years for uranium-238 to decay into thorium-234, how can the decay rate be measured? What intermediate activity is taking place that would give an indication of the time it would take an atom to decay into the next element in the decay chain?

We assume (based on some very convincing theory and a tremendous amount of observation of decay rates) that the probability of any single nucleus decaying in any given second is constant. That is, the individual nuclei don't "get old" and more likely to decay as they "age" - it's not like humans where the mortality rate varies over an average lifetime.

So all we need to compute the half-life is the probability that any given atom will decay in the next second. We find that by observing a very large population of atoms; even a moderate-sized chunk of U-238 weighing a few kilograms contains on the order of $10^{25}$ atoms. A half-life of 4.4 billion years corresponds to something well north of one million decays per second in a sample that size.

Actuarial science should be so lucky

 

[russ_watters]

I understand how the half-life works. I don't understand how it could be determined that it takes 4.4 billion years. We obviously can't measure something that takes that long. So how is it done? How do we know it takes 4.4 billion years. I'm obviously missing some important step.

It is OK not to know how the half life works: that's why you are here! It meas some atoms decay in a much, much shorter time and some in a much longer time. 4.4byr is just the average. So we can always see some decaying now and by comparing how many you see decaying to how many you have, you can compute the half life.

 

[sophiecentaur]

Working out the half life when it's extremely long may seem impossible. However, it's not 'too' hard. If you take a sample of your isotope and you know its mass, then you know how many nuclei there are. You then just measure the rate of decay, counting the clicks on Geiger Counter. That will tell you the fraction of the total number of nuclei that are decaying per second (or minute / day / week). That is easy to convert to ' half life' and you don't ned to wait a billion years!

 

[HallsofIvy]

Any given atom of Uranium-238 has a very low probability of fissioning in the next few minute. But there are a heck of a lot of atoms in a gram of U-238! Knowing how many atoms there are and knowing how many fissioned in the last, say, several hours, we can calculate the probability that anyone will fission in an hour and so find the half-life.

 

[dmehling]

How does one calculate the number of uranium atoms in a chunk of rock to begin with?

 

[russ_watters]

How does one calculate the number of uranium atoms in a chunk of rock to begin with?

First purify it, then weigh it, divide by the molar mass and multiply by Avogadro number.

 

[enorbet]

This is lately a particularly important measuring tool since so many attackers of Science hate the concept of Deep Time and contend that we would require a time machine to actually observe say a 5000 year half life. However they assume some scientist just made up this measuring stick and disregard that it was basically stumbled upon and worked out over many years, some say beginning by 1860, but surely by 1900. They disregard that some radioactive elements have extremely short half lifes, easily observed in one human lifetime. By determining that constants are at play in all radioactive decay it is not at all unreasonable to conclude that what is accurate to 100 years will also be accurate to 200 years, and so on. Furthermore no matter what radioactive element we choose to date an object, they all agree out to their limits of accuracy.

Some of the same people who recognize that if we observe a water tower of 1000 gallons that is subject to a leak (or evaporation loss) of 1 gallon per minute it is trivial to determine when the tower will be empty, somehow have problems with observing DPM, radioactive decay, and concluding half life times.

I have heard many say things like "Well, C14 dating isn't THAT accurate" when trying to defend a belief that the Earth is 6,000 or 50,000 years old. I find this particularly ignorant and abhorrent since it displays near hatred, let alone disrespect, of scientists and under it all The Scientific Method. I ask them if they have ever used a ruler to measure something and if they would be satisfied with a ruler that stopped divisions at a centimeter or even an inch - no decimals or fractions. They invariable answer "No!" upon which I ask them if they suppose that scientists holds themselves to such monstrously lower standards that they would rely on a measuring tool that was, not 10% inaccurate, not 90% inaccurate, but factors in the millions.

Thankfully we have such commonly available shows like Cosmos 2014 attempting to make clear the nobility of struggle that is Science, but IMHO it is shameful that we even have to address such hatred and ignorance in modern society. It's not that I expect every Average Joe walking the street to fully comprehend radioactive decay, but rather the blatant disregard for the integrity of the giants upon whose shoulders we all stand.

I apologize if my comment devolved into something akin to a rant, but this does get my dander up. To be clear, I respect OP for asking a reasonable question. That is how it should be. That is consistent with Science at it's most fundamental form.

 

[dmehling]

For the record, I am actually skeptical of deep time geology. That is based on my theological presuppositions. Yet, I am also a devout believer in science and the scientific method. Unlike many in the creationist movement, I recognize that radiometric dating poses a major challenge to my understanding of Earth history. Such dating methods are based on good scientific reasoning and experimental data. I do not think that scientists are guilty of misrepresenting their findings regarding radiometric dating.

Having theological beliefs in opposition to the current scientific consensus does leave me in an intellectually awkward position. That is what compels me to study this subject. I wish to fully understand it before I can begin looking for possible inconsistencies. I'm not interested in simply debating the issue, but I want to find the truth, no matter where it leads me. That is the only responsible thing to do.

 

[Drakkith]

This may interest you, Dmehling.

http://www.talkorigins.org/faqs/dating.html

 

[ZapperZ]

I understand how the half-life works. I don't understand how it could be determined that it takes 4.4 billion years. We obviously can't measure something that takes that long. So how is it done? How do we know it takes 4.4 billion years. I'm obviously missing some important step.

How do you think that we know we can send a spacecraft to Jupiter or any of the planets when we had never done that before?

The missing step here is the apparent lack of understanding of the exponential decay description.

And before this thread gets into trouble, I will warn that the topic MUST be on physics and not divert to opinion about your own beliefs.

Zz.

 

[russ_watters]

I will give kudos, though, to both enorbit for sniffing that out (I was ready to yell at you for not giving dmelhing the benefit of the doubt!) and to dmelhing for asking the questions and listening to the answers in an open/honest way and for being open about your bias.

 

[enorbet]

I will give kudos, though, to both enorbit for sniffing that out (I was ready to yell at you for not giving dmelhing the benefit of the doubt!) and to dmelhing for asking the questions and listening to the answers in an open/honest way and for being open about your bias.

This thread has given me cause to be very pleased with my recent decision to come here to PF. Actually, my response wasn't at all directed at dmelhing but at the conflict he so carefully and reasonably describes. I have nothing but respect for dmhelhing and his quest for truth. I also have some respect for moderators here who apparently don't assume their members are badly behaved children unable to come to some reasonable conclusion, even when things get emotional.

It says to me that there is some recognition here that truly understanding text-only communication is difficult and fraught with many forms of translation problems, ie: language, culture, context, not to mention sacred cows. It is difficult enough to fully understand what someone really means when we have body language, tone of voice, etc. let alone absent such context.

This rather punctuates the value of Science, since it is testable and falsifiable, so that text and numbers exact meaning can be determined and weighed and the person becomes "transparent" or at least not part of the equation. It also has considerable bearing on this exact thread since there is nothing basically wrong with Philosophy, even speculation and spirituality reserved for arenas in which we have yet to have the ability to do Science, apply Reason.

It seems to me it is many times more difficult to determine what some ancient person(s) really meant with their choice of words, than say... translating the Curie's journals. (See? In case someone didn't notice - I did wink after all - this last bit was my feeble attempt to actually come full circle and address the Topic )

Barkeep! Kudos all around!

 

[dauto]

May be worth pointing out that radioactive dating is not the only strong evidence for deep time. The age of the universe for instance has been accurately measured (3 sig figs!) by astronomical/astrophysical/cosmological techniques that do not depend of radio dating at all and have come up with very consistent results pointing to deep time.

 

[UltrafastPED]

One method is described here:
https://hps.org/publicinformation/ate/q8270.html

This requires a chemically pure sample, its mass, and a record of decays - so it is important to isolate the sample during the counting process.

 

[basheer uddin]

this may be helpful
http://www.britannica.com/EBchecked/topic/489089/radioactivity/48294/Measurement-of-half-life
https://hps.org/publicinformation/ate/q8270.html

 

[jtbell]

I'd like to remind everybody about Zz's comment:

And before this thread gets into trouble, I will warn that the topic MUST be on physics and not divert to opinion about your own beliefs.

I see this as including both pro- and anti- "young Earth creationism" comments. We don't get into those sorts of discussions here, nor discussion of religious beliefs in general.

I've deleted some posts accordingly.

 

[sophiecentaur]

I'd like to remind everybody about Zz's comment:



I see this as including both pro- and anti- "young Earth creationism" comments. We don't get into those sorts of discussions here, nor discussion of religious beliefs in general.

I've deleted some posts accordingly.

It has to be OK, as long as the word "Creationism" is not used, surely, or we could not discuss anything involving periods of time greater than a few thousand years. It is a difficult path to steer. I have to admit, if PF is to avoid becoming like a thousand other sites.

 

[abitslow]

{Edit: abitslow: I have edited the formatting of your post to add blank lines and quotes to make it easier to read. Please consider using these in future posts. Otherwise, your post looks like one big lump of a continuous paragraph. - Zz.}

If it takes 4.4 billion years for uranium-238 to decay into thorium-234...

This is wrong. As already said, but perhaps in a way that is not clear and plain enough.

This is equivalent to saying that since the average life expectancy is 80 years, then it will take Bob 80 years to die. A particular atom of U-238 may decay now, may decay in 10 years, or 1000 or 1,000,000 or 100,000,000,000,000,000,000. All half-life can talk about is the average for a (large) group of atoms.

If you do the math for a mole of U-238, that is 6E23 atoms, from the calculation it is apparent that measuring a sample for a couple of minutes will give you a very good statistical average. ( Assuming that the probability of decay is constant, it is a simple matter to determine what half life is for atoms with half-lives well into the billions of years (given enough of a sample).).

I don't understand why many of the posts haven't been removed for being off topic and not Physics, but I want to point out that you are unlikely to have a better shot at undermining the science about deep (pre)history as the top scientific minds that the Vatican has thrown at the same question. It is good that you are questioning it, as you will see that there are several assumptions about the constancy of the Laws of Physics over time, and their independence from other influences. It is virtually certain that you will discover nothing new here by analysis of the known facts, too many great minds have already tried that. It is possible that by going out and gathering NEW facts (or recognizing the applicability of 'unrelated' facts) you will advance the science. Go get 'em, tiger!

 

[dmehling]

It's been a while since I started this thread, and I have not been able to do much study of the subject in the time since. However, I want to take another look at it, and so I would like a few words of advice on where to find good online resources. I have never taken a physics or geology course at the college level, which puts me at a great disadvantage. But if I wanted to start learning some basic physics concepts in order to begin understanding radiometric dating, where should I begin?

 

[russ_watters]

... I want to take another look at it, and so I would like a few words of advice on where to find good online resources. I have never taken a physics or geology course at the college level, which puts me at a great disadvantage. But if I wanted to start learning some basic physics concepts in order to begin understanding radiometric dating, where should I begin?

I'd get a freshman physics textbook or find some online texts/lecture notes and skip to the sections about radiactive decay. I skimmed this and it seems to me to have everything you should need: http://www.physics.rutgers.edu/~steves/161/lectures/Lecture_20.pdf

From your initial questions, the issue you are having appears to be one of math, though, so I see a possibility that you may have trouble with the sample problems. The issue appears to be in understanding how we can take a small (in timeframe) amount of data and from that extrapolate a pattern that extends much longer.

 

[dmehling]

What type of math? Calculus?

 

[russ_watters]

Have a look at the link. It's just algebra.

 

[sophiecentaur]

where should I begin

I think your problem is that you may need to begin a 'boringly long way' back in the process. The relationship between rate of emission from a sample and probability of a single nucleus decaying is, I would say, pretty sophisticated stuff - when approached without the back knowledge. But you can always just accept it, in the same way that you (and most of the rest of us) probably accept things like the Cosmological 'facts' we get bombarded with - such as how far it is to the nearest Galaxy and the age of the Universe.
But then there can be a problem coming to terms with how unsatisfactory that may be. Join the club.
One point I could make and that is that you can start at an elementary level and 'prove for yourself' some of the easier bits of Physics - like how levers work (quantitatively) and how confirming, a calculation of how much water you can heat up with your heating boiler etc. etc. . Eventually, you may find that you can 'believe' that other stuff can be predicted from theory, without actually knowing the theory. Note, I am not being patronising here; that statement is based on personal experience, which has allowed me to rely on what clever (creditable) people tell me. People who fail to do this end up as Climate Change Deniers and Creationists.

 

[STOKER]

For the record, I am actually skeptical of deep time geology .

Hi dmehling,
I'm not a physicist, and I'm also way out of my league intellectually just visiting here, but I just completed a geology degree so I might be able to make a useful contribution to this thread. Absolute age of the Earth is determined by zircons in volcanic ash beds and lava flows (rhyolitic through to andesitic geochemistry). Zircons (zirconium silicate) are isomorphic minerals which are lattices of silicate tetrahedra, which have gaps (between the clusters of tetrahedra) large enough to fit zirconium cations. They can also substitute uranium cations (hence isomorphic), but not lead cations, as leads ionic radius is too big (so any lead in the zircon is due to radioactive decay of the uranium). When this cools it reaches closure temperature, and radioactive decay begins. Another great thing about zircons is that they have a high melting point so are unlikely to be "reset" by metamorphic heating, and are incredibly durable and resistant to weathering. As you know there are several decay paths so the age of each zircon can be "cross-checked". There are other ways of absolute dating - in basalt flows - due to the rarity of zircons in mafic lavas, geologists use argon/argon in plagioclase or whole rock.
Which bit of that are you sceptical about?
Geology has a surfeit of other phenomena which can only be explained by deep time. Here's a couple off the top of my head: limestone (which forms on carbonate platforms under the sea), currently situated 5 km above sea level in New Guinea (and I'm talking entire mountain tops of the stuff - complete with marine fossils) - I'll leave it to you to ponder how long that process would take. Or magnetic striping in ocean floor basalts recording switching of polarity of the Earth's magnetic field, extending literally thousands of kilometres either side of the spreading ocean ridges capturing a continuous polarity reversal record for 180 million years, complete with age correlated fossils in the sediments above the bands.