What is Decay constant: Definition and 26 Discussions

A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant:





{\displaystyle {\frac {dN}{dt}}=-\lambda N.}
The solution to this equation (see derivation below) is:







{\displaystyle N(t)=N_{0}e^{-\lambda t},}
where N(t) is the quantity at time t, N0 = N(0) is the initial quantity, that is, the quantity at time t = 0, and the constant λ is called the decay constant, disintegration constant, rate constant, or transformation constant.

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  1. E

    B What is meant by decay constant?

    Hello everyone. First my english is not good, sorry for that. So i am not a physician, i am just somebody who wants to learn things by myself, and therefore i don't have many people to ask from, if i am stuck. So here it goes. There are many threads about this question already, and i am still...
  2. A

    B How are activity and decay constant different?

    What's the difference between activity of a radioactive sample and the decay constant. Both are measured in second inverse. Please distinguish among the two?
  3. WhiteWolf98

    Activity of 1 g of carbon if 1 in 10^12 atoms are carbon-14

    Homework Statement Carbon-14 decays by β emission and has a half-life of 5570 years. What is the decay constant of carbon-14? What is the activity of 1 g of carbon if 1 in 1012 atoms are carbon-14? After what time will the activity per gram have fallen to 3 Bq? Homework Equations λt½ = ln(2)...
  4. A

    I Dimensions of the pion decay constant

    The pion decay constant f_{\pi} is defined by <0|\overline{d}\gamma^{0}\gamma^{5}u|\pi^{+}>=f_{\pi}m_{\pi} where I have set the momentum \boldsymbol{p}=0 (and used the temporal component of the axial vector). Now, at the right-hand-side the dimension is two (the decay constant and the mass are...
  5. moenste

    Nuclear equation of the decay, decay constant, # of atoms

    Homework Statement A sample of iodine contains 1 atom of the radioactive isotope iodine 131 (131I) for every 5 * 107 atoms of the stable isotope iodine-127. Iodine has a proton number of 52 and the radioactive isotope decays into xenon 131 (131Xe) with the emission of a single negatively...
  6. S

    Co-60 Unit Activity: Treatment Time Calculation

    Homework Statement A patient is treated for cancer using radiation from a cobalt-60 unit. Exactly 1.5 years later another patient is treated for the same cancer using the same co-60unit previously used. How much longer would treatment be for the second patient? Homework Equations Decay...
  7. Kingyou123

    Determine the value of a decay constant

    Homework Statement What's up guys, I'm stuck on #2 of this worksheet,http://luc.edu/faculty/dslavsk/courses/phys111/homework/phys111-2015hw1.pdf The half - life of C - 14 is 5730 years. Determine the value of its decay constant (and express the answer in appropriate MKS units). 2.The attempt...
  8. CivilSigma

    Is the decay constant , constant for all isotopes of element

    I have this true and false question: " The half life and therefore the decay constant will be the same for every isotope a) True b) False c) only if it is an isotope of the same element " I think this is false, just by intuition.
  9. S

    How Does the Decay Constant Influence Water Flow in Exponential Decay Models?

    When modelling exponential decay in class we did a water flow through a burette experiment. We were given the equation V(t)= V0 e^-λt and ln(V0/V)=λt Where lambda is the decay constant, V0 is the initial volume and V is the volume at any time t. What does the decay constant actually tell you in...
  10. P

    Calculating Decay Constant and Amount of Thorium Plated

    Homework Statement A small quantity of the thorium isotope Th(A=228, Z=90) (half-life 1.913 y) is prepared and electroplated onto a thick sheet of copper and overcoated with a thin film of gas-tight polymer. The plating and coating are both thin enough so that none of the alpha particles...
  11. G

    Can G-Parity Explain the Dominance of Vector Current in Tau Decay?

    I'm studying the \tau \rightarrow \rho \; \nu_{\tau} decay. I'm asked to calculate the decay width, using a parameterization of the matrix element of the hadronic current. I actually find a matrix element of the form: \left<\rho |\; \bar{u} \gamma^{\mu} \left( 1-\gamma^{5} \right ) d \; |...
  12. N

    Can a Decay Constant be bigger than 1?

    Decay Constant, as it says on my revision sheet is defined as 'The probability of a nucleus decaying per unit time'. Does it mean that it can't be greater than 1? Otherwise, doesn't that imply that a nucleus is most certainly going to decay(greater than 100% chance within a certain period...
  13. F

    Calculating Decay Constant Without Initial Value

    Radioactive sample activity is said decreases by factor 5 during 2-h interval. How to find the decay constant? If the given initial value is not given? I don't know how to calculate.
  14. F

    Calculating half life (Decay Constant)

    Homework Statement The activity of a radioactive nuclide drops 78.5% of it's initial value in 2000 years. Homework Equations I know I need to use the decay constant to work out my answer so I have re-arranged the equation as illustrated in my picture, the only problem is I cannot...
  15. E

    What is meant by 'decay constant'?

    Hi, My textbook states a decay constant of an isotope as 3.84 x 10 to the minus 12 - per second. Surely decay constant can't be the number of decays per second because that wouldn't stay constant. As the isotope decays there are less atoms to decay and therefore the rate reduces. So...
  16. S

    How Do You Calculate the Decay Constant of Copper 66?

    Homework Equations I was given all this information... I cannot figure it out whatsoever. I would post my attempts but there were too many. Any ideas would be helpful. I know the answer is 5.09 as the half life Decay Constant of Copper 66 Sources do not emit radiation at a constant...
  17. S

    Nuclear physics - decay constant

    Homework Statement Hello. Im having a problem here, i got a sample of Au nucleis. I'm bombing them with neutrons and each second 20^10 of them undergo a reaction where they turn radioactive. Im trying to look at this problem as if i would have a sample of radioactive materia which decaying to...
  18. R

    Radioactive Decay: Mean Life Time & Decay Constant

    How can we prove that the mean life time of a radioactive decay is reciprocal to the decay constant?
  19. R

    Muon Decay Constant: Find Mean Lifetime & Lambda

    muon decay constant/ muon flux where can i find the decay constant of a muon (the lambda which appears in): http://upload.wikimedia.org/math/3/f/2/3f28b1c0d4362b86a89f976d83d81070.png thanks edit: oh the wiki page http://en.wikipedia.org/wiki/Exponential_decay gives the relationship...
  20. I

    Need help understanding Half life, decay constant & activity equations

    Hi guys i'm having much difficulties in understanding the relations between half life, decay constant and activity. I'll explain what i known here. T^{\frac{1}{2}} is the half life which is the time to reduce the nuclides by half. \lambda is the decay constant which can be solved...
  21. N

    What would the value of the associated decay constant be?

    Homework Statement If a numerical value had to be assigned to the half life of 27Al, what would that value be? What would the value of the associated decay constant be? What does this mean about the activity of 27 Al? Homework Equations The Attempt at a Solution Since it is a...
  22. S

    Radioactivity and decay constant

    A piece of radioactive substance gives a received count rate of 6000 counts per minute in a detector whose efficiency is known to be 5%. If the sample contains 10^10 atoms, what is the decay constant ( λ ) of this radioactive substance ? No idea how to solve this problem. Any help would be...
  23. M

    Using differential equations to determine the decay constant for carbon-14

    Homework Statement Q(t) is the amount of carbon 14 at time t. Given half life of 5730 years, and assuming that Q satisfies dQ/dt=-rQ; determine decay constant r Homework Equations The Attempt at a Solution I solved the differential equation and got Q=ce^-rt. Now what? And hints/help?
  24. M

    Derivations of the Decay Constant Equation.

    I have used this equation in the past but have no knowledge of how the equation is formed. I will probably learn about it next year, but that is a long time to wait for a burning question. :shy: Here is the equation I am talking about. I would like be sure that I know what everything stands...
  25. E

    Calculating the Decay Constant of Carbon 14

    Carbon14 has a half life of 5730 yrs. This is the only information i am given. Caluculate the decay constant of Carbon 14. This is what I have done. dN/dt = -lambda(N) I know the Avogadro Constant is equal to 6x10^23 So i am using 1kg in my formula. 14C = 6 x 10^23 x 1000/14...