Half-life Definition and 133 Threads

Half-life (symbol t1⁄2) is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential or non-exponential decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life is doubling time.
The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s. Rutherford applied the principle of a radioactive element's half-life to studies of age determination of rocks by measuring the decay period of radium to lead-206.
Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.

View More On Wikipedia.org
Recent contents Top users
  1. B

    Textbook 'The Physics of Waves': Lifetime of SHM Oscillators

    Reference textbook “The Physics of Waves” in MIT website: https://ocw.mit.edu/courses/8-03sc-...es-fall-2016/resources/mit8_03scf16_textbook/ Chapter 2 - Section 2.3.2 [Page 47] (see attached file) Question: In the content, it states that the lifetime of the state in free oscillation is of...
  2. Kairos

    I Radioactivity in quantum physics

    In a block of 1 kg of radioactive material that has reached its half-life, are the atoms in a superposed disintegrated/undecayed state (50-50), or are they all individually determined (50% disintegrated and 50% undecayed) before observation ?
  3. RobinBanks

    I Speeding up the half-life of plutonium

    I know that it is possible to speed up the half-life of plutonium with neutrons. Who can tell me more about this? Thoughts on harnessing this power to decay plutonium so it's unusable in nuclear weapons?
  4. I

    I Neutrino-Nucleus Interactions and Half-Life Constraints

    At what half-life duration, if any, does the likelihood of a neutrino collision within a sample of radionuclide atoms exceed the likelihood of a decay event in those atoms over the same time period? Can they be efficiently excluded by their reaction products, or are they meaningfully difficult...
  5. Aromalsp

    I Decay constant of Different Elements and Isotopes?

    Different elements and isotopes have different rates of beta decay because the half-life of the element or isotope reflects its stability, which is determined by the nuclear force between the protons and neutrons in the nucleus of the atom. The number of protons and neutrons affects the balance...
  6. D

    A "Cross-section" and "half-life" of excited states

    Hello, I work with a spectrometer that does ionizations through laser 2+1 photons resonant ionization (a high power narrow bandwidth laser is tuned to a precise wavelenght so that it allows reaching an excited energy level of a particular element with the sum of two photons absorbed...
  7. A

    I Particle lifetime (half-life) question

    If I have a particle with a average lifetime of 15min, if I take 10 particles confined in a box, after 15 min there will be 5 particles. After 15min 2.5 particles and so on... , but so, at the end there will be the last particle that decades. That particle lived far longer than 15min, but is the...
  8. H

    Chemistry Calculate the half-life of the antibiotic Ofloxacin in this patient

    A 70 kg patient is treated with ciprofloxacin (2 x 500 mg / d) for an infection pulmonary. Ciprofloxacin is an antibiotic eliminated primarily by the kidneys, its apparent volume of distribution is 3 [1 / kg) and its clearance is 0.5 (Wh x kg). Calculate the half-life of ofloxacin in this...
  9. CPW

    B Shorter half-life and therefore very radioactive -- why?

    In reading through The Physics of Energy, the textbook describes the decay chain of U-238: "The longest half-life of any descendent in the chain is less 1 million years. Many half-lives are much shorter, making those nuclides very radioactive." Why does having a short half-life make a...
  10. S

    I Unbihexium could have a half-life of millions of years?

    This article seems to say that the range of estimates go this high. This could be something that would actually stay around long enough to be of some use. https://www.chemistryworld.com/news/beyond-element-118-the-next-row-of-the-periodic-table/9400.article
  11. S

    How Is the Variance Used as Weight in Half-Life Error Analysis?

    What is meant by the constant background and how would one deduce the half-life IF not from the fit?
  12. G

    What happens if t is greater than half-life?

    I tried plugging into the equation t = 3t1/2 and I got A(t) = 0.125A0 since -lambda*t = - ln(2)*t/(t/3) = -ln(2)*3. So I understand that there will be 12.5% left of the original value since three half-lives have passed. But then I realized this won't help me answer the question much. So I'm...
  13. E

    Laser pulses could reduce the half-life of nuclear waste to just 30 minutes

    If this could actually be achieved, it would probably win him another Nobel prize, and solve the dilemma of nuclear waste for good. https://bigthink.com/technology-innovation/laser-nuclear-waste?fbclid=IwAR1mFH03XE1x744PHRXCKfWmBt2qeRquOYMAgIXUjqSVEK1kqK2hSkUktcg
  14. A

    What’s the relation between activity and half-life

    I’m confused because there are two equations: 1) A=λN 2) A=A0exp^-(λt)If half-life increases, λ decreases, and A decreases according to 1); but, If half life increases, λ decreases, hence exp^-(λt) decreases, A should decreases according to 2)Why is this so? Where went wrong? Thanks!
  15. Mackenzie Cobb

    Chernobyl Cesium 137 Half-Life vs. Chernobyl Contamination

    Let me start out by saying that I have no idea what I'm talking about. I graduated from Indiana University with a Bachelor's in Spanish, and I work as a Loan Review Specialist at a bank, which has NOTHING to do with my degree, and still yet nothing to do with this topic. But lately, I've become...
  16. Bystander

    Half-life of the "novichok" nerve agent outside of a body?

    What is the half-life of "novichok" in, and outside, a biological system? There seems to be an "epidemic" of "novichok" poisoning in Great Britain lately, and given that it's a nerve agent, my understanding is that it should be susceptible to fairly rapid decomposition/breakdown.
  17. H

    [Poisson Stats] Error on half-life for radioactive decay

    Hi there, not sure whether this is in the right section but: I've made two runs of a radioactive decay experiment where I've got a log(N) vs. time plots. From this I've got the decay constants and hence the half-life. I've averaged these two half-lives ( = 160 secs) and now I'm trying to work...
  18. C

    Finding the Half-Life of a Radioactive Element

    Homework Statement In 2 years, 20% of a radioactive element decays. Find its half-life rounded to 2 decimal places. Homework Equations A(t)=a*e^kt The Attempt at a Solution The only thing I've been able to figure out is k=LN(0.2)/2
  19. G

    Half-life using Schrodinger's wave equation

    Hello guys! I've been learning how to estimate half life using Schrodinger's time-independent wave equation. In class, we divided the energy barrier into five smaller segments just like this webpage http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/alpdet.html#c1 I was wondering if we could...
  20. S

    I Fusion half-life of diprotium molecule

    A diprotium molecule might undergo tunnelling to fuse by two reactions: p+p→d+e++νe p+p+e→d+νe What is the half-life for the fusion of an isolated diprotium molecule in its ground state (vibrational and rotational)? Naturally big, but also naturally finite. And might be computed. An estimate...
  21. L

    How do I use this equation? Estimating half-life of a decay

    How should I go about using equation 8.18? Link can be found below. In the book, an example is used where Th-220 --> C-12 + Po-208 with a Q value of 32.1 MeV is used, and it is said to yield t1/2 = 2.3x106 but for the life of me I cannot reproduce this result. This is what I did: Going from...
  22. N

    Shouldn't Carbon-14 concentration be the same everywhere?

    Why is it that newer organic matter has more carbon-14 than older organic matter? Isn't carbon constantly recycled, because of the carbon cycle? So C14-depleted carbon from old matter would enter the atmosphere, then be breathed in by new organic matter. The new matter would start off with...
  23. M

    Half-Life & Flux: Is Decay Formula Relevant?

    Given an initial mass of some isotope subjected to a constant neutron flux, how fast will the mass drop off? Would not the survival curve look exactly like the curve for radioactive decay? Both cases describe a starting mass subjected to a constant transformative force at a rate that depends...
  24. wolf1728

    End Amt =Start Amt *e^-0.0391 * t (in years) Half-life =?

    I know how to do half life problems and I even have a half-life calculator on my website: http://www.1728.org/halflife.htm However, I cannot calculate half-life when problems are stated in this form: End Amt = Start Amt * e^-0.0391 * t (in years) Half-life =? I know calculus but I find it...
  25. InsaneScientist

    Time taken for amount of a nuclear material to remain

    Homework Statement The half life T½ of Carbon-14 is 5730 years. What is its decay constant? After what length of time will 35% of an initial sample of Carbon-14 remain? Homework Equations Decay constant λ= 0.693 / T½ Where N = amount of radioactive substance, N=N0e-λt The Attempt at a...
  26. Alejandro Golob

    Error Propogation for Half-Life

    In this homework question we are told to calculate the half-life of an isotope based on count-rates before and after a given time interval, the relevant equation is given below. Half-life = t1/2 = tln(2)/ln (A/A0) The second part asks to determine the standard deviation of the half-life due...
  27. G

    What is the half-life of proton decay in order to detect 3 decays in one year?

    Assume you want to find experimental evidence of the proton decay. For this, you use a cylindrical tank with 36 meters high and 17 meters radius which is full of water (18 g / mol). Around the tank are detectors whose overall detection efficiency of a proton decay that gives within the deposit...
  28. L

    Muons hitting Earth half-life explanation in SR

    Muons time dilation from the Earth's frame (and length contraction of Earth's atmosphere from muon's frame) is the usual explanation of the fact that muons reach the Earth when they shouldn't just by their rest half-life. My question is if the explanation based on differential aging(different...
  29. J

    Partial Half-Life of 22Na: Ec & β+ Emission

    Homework Statement What are the partial half of 22Na for decay by a)Ec b) β+ emission Homework Equations λ=ln2/T1/2 The Attempt at a Solution this what I do T1/2 =2.602 Yr λ=ln2/2.602 λ=0.266 yr-1what is the difference between a)Ec b) β+ emission there is no Percentage of each decay type.!
  30. danihel

    Do hadron particles have half-life?

    Hi, i heard that as the universe will expand and the energy will grow sparse, in the end the matter itself will turn into radiation that will loose energy. So i wanted to ask, can a proton decay? and is it the same phenomenon as radioactive decay? Does it mean that even hydrogen (with no...
  31. U

    Why doesn't Rubidium decay to Strontium?

    Both ##^{87}_{37}Rb## and ##^{87}_{38}Sr## are odd-even nuclei, so we can ignore the pairing term ##\delta##. I tried to calculate the most stable Z for a given A by finding ##\frac{\partial B}{\partial Z} = 0##. That gives the most Z-stable value of ##Z_0 = \frac{2\gamma A}{4\gamma + \epsilon...
  32. Mark lamorey

    What is the meaning of unbound in the context of half-lives of nuclei?

    I have been looking at half-life of various isotopes and many of the tables / information I am finding is giving energies (MeV, KeV) for certain half lifes. This does not make sense to me, am I missing something ? For example : http://ie.lbl.gov/toi/listnuc.asp?sql=&A1=5&A2=5 5Li and 5He give...
  33. S

    Estimating Half-Life of Alpha Decay: Nucleus ##^{252}_{98}Cf##

    Homework Statement Nucleus ##^{252}_{98}Cf## alpha decays with half life time ##t_{1/2}=2.6## years. What is the velocity of the alpha particle after the decay? Estimate the half life time of the nucleus after the decay. Homework EquationsThe Attempt at a Solution Ok, no worries about the...
  34. Calpalned

    Is half-life inversely related to the radiation dosage of an element?

    Is half-life inversely related to the radiation dosage of an element? That is, if an element has a longer half-life is it safer? If so, why is plutonium so dangerous, even though it has a very long half life
  35. A

    Factors which influence to half-life speed

    Looking for researches, articles and experimental values conserning factors which influence to half-life speed for different isotopes.
  36. M

    Uncovering Half-Life Data for Odd Isotopes: A Search for Fission Products

    The Sigma database at Brookhaven lists seven isotopes as fission products for which I can't find half-life data. I've tried nea6287-JEFF-20-1, the NuDat_2 web site, Nuclear Wallet Cards and Wikipedia. Anybody have any other ideas? The isotopes are 74-As-m1 85-Se-m1 86-Br-m1 109-Ru-m1...
  37. T

    Is There a Shortcut for Solving Half-Life Decay Equations?

    A 100 mg sample of magnesium-27 decays by 7% of its previous mass every minute. Determine its half-life and start the half-life decay equation. The textbook that I got this from (Nelson Physics 11) tells me the answer, but uses a long and annoying process to find it: creating a table at...
  38. Greg Bernhardt

    Half-Life: Definition, Equations, and Extended Explanation

    Definition/Summary The half-life, t_{1/2}, of an inverse exponential process (an exponential decay) is the time taken for the amount to reduce by one-half. It is constant. Processes with a half-life include radioactive decay, first-order chemical reactions, and current flowing through an...
  39. M

    What does a radionuclide with a short half-life mean?

    I don't understand what this means? Including artificially produced nuclides, more than 3300 nuclides are known (including ~3000 radionuclides), many of which (> ~2400) with decay half-lives shorter than 60 minutes. This list expands as new radionuclides with very short half-lives are...
  40. K

    How long does it take for the activity of the radionuclide to decrease by 50%?

    Homework Statement The activity (decays per second) of a certain radionuclide is observed to decrease by 87.5% in 30 hours. What is the half-life of the radionuclide? Homework Equations (1) A(t) = A_{0}e^{-λt} (2) T(1/2) = 0.693/λ The Attempt at a Solution I'm just stuck on...
  41. J

    MHB Half-Life of Radioactive Waste: 150,000 Years

    After 150 thousand years, only 1/8 of the original amount of a particular radioactive waste will remain. The half-life of this radioactive waste is how many thousand years? 150,000 years / 1/8 150,000 / .125 = 1,200,000 If this isn't correct is the 1/8 suppose to be stay as a fraction, turned...
  42. P

    Half-Life Formula: Is It Possible?

    Hi, I have always wondered, is there a known formula that predicts the half life of an atom based on known values (e.g., number of protons and neutrons) rather than observation?
  43. D

    Deriving Error Equations for Half-Life Calculations

    Homework Statement How to derive an error equation: t1/ 2 = ln 2/λ= 0.693/λ. Confused, and don't even know where to start. 2. The attempt at a solution σ(t1/2)= σ(ln2)/(ln2) + σ(λ)/λ
  44. H

    Is this half-life answer kosher?

    Question: U has a very long half life and decays through a series of daughter products ending with a stable isotope of lead. Very old samples of U ore, which have not undergone physical or chemical changes, would be expected to show an equilibrium between the daughter elements provided that...
  45. M

    What is the next step after finding the k-value in half-life calculations?

    Maybe this is a dumb question... Let's say I want to figure out the age of a rock and I have the half life of an element. If I have this equation y(t)=e^{kt} where first I figure out the k-value using the half life. That part I get. Now that I have the k-value I 're-use' the formula...
  46. G

    Proving the half-life of Potassium-40

    Homework Statement "K-40... decays by two radioactive processes. It can decay by electron capture or β- emission. It is found that a sample containing 4.0x10^18 nuclei of K-40 emits a total of 68 β- particles and photons each second. This shows the half life is 1.3x10^9 years." Use the...
  47. rakeru

    Finding Mass of Isotope After Radioactive Decay by Half-Life

    Homework Statement A radioactive sample contains 2.25g of an isotope with a half-life of 3.8 days. How much of the isotope in grams will remain after 11.0 days? Homework Equations The Attempt at a Solution Hi! I've just started college this semester. I'm taking Introductory Chemistry. Right...
  48. M

    Hello,I'm revising half-life for GCSE and have come across some

    Hello, I'm revising half-life for GCSE and have come across some questions regarding fractions. For example, "what fraction of the original nuclei will still be unstable after 5 half-lives?" Am I right in thinking it would be 1/20 as 1/2 x 5 = 1/20 or is that too simple? Thanks, Molly
  49. D

    Fotran program to find half-life of a radioactive material

    Homework Statement I need to write a program that, given the decay constant of a radioactive material, will calculate numerically (to withing one second) the time taken for half of the orginal sample of material to decay.Homework Equations λ = decay constant C0 = start amount of material...
  50. D

    Half-life decomposition, find final concentration

    Homework Statement In a first order decomposition in which the rate constant is 0.03 sec-1, how much of the compound (in mol/L) is left after 39 sec, if there was 2.00 mol/L at the start? I'm using a few equations and trying to plug it in but I don't know whether they are appropriate or not...
Back
Top