A simple question about radioactive decay

  1. 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?
  2. jcsd
  3. You can measure the decay rate of a known amount of the isotope.
    From this you can calculate the half-life time.
  4. Drakkith

    Staff: Mentor

    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?
  5. 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.
  6. Nugatory

    Staff: Mentor

    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 :smile:
  7. russ_watters

    Staff: Mentor

    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.
  8. sophiecentaur

    sophiecentaur 14,712
    Science Advisor
    Gold Member

    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!!
  9. HallsofIvy

    HallsofIvy 41,264
    Staff Emeritus
    Science Advisor

    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 any one will fission in an hour and so find the half-life.
  10. How does one calculate the number of uranium atoms in a chunk of rock to begin with?
  11. russ_watters

    Staff: Mentor

    First purify it, then weigh it, divide by the molar mass and multiply by Avogadro number.
  12. 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.
  13. 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.
  14. Drakkith

    Staff: Mentor

  15. ZapperZ

    ZapperZ 30,731
    Staff Emeritus
    Science Advisor
    Education Advisor

    How do you think that we know we can send a space craft 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.

  16. russ_watters

    Staff: Mentor

    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.
  17. 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. :wink: (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 :smile: )

    Barkeep! Kudos all around!
  18. 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.
  19. UltrafastPED

    UltrafastPED 1,912
    Science Advisor
    Gold Member

  20. jtbell

    Staff: Mentor

    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.
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