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Need help understanding Half life, decay constant & activity equations

  1. Jan 17, 2010 #1
    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.

    [tex]T^{\frac{1}{2}}[/tex] is the half life which is the time to reduce the nuclides by half.

    [tex]\lambda[/tex] is the decay constant which can be solved from

    [tex]\lambda[/tex] = 0.693/ [tex]T^{\frac{1}{2}}[/tex]. Am i correct? Where do 0.693 come from?

    The decay/sec can be find out using [tex]A = -\frac{dN}{dt} = \lambda N[/tex] if the half life and N is known.

    I want to clarify N is in grams? So like 10g of C14 would be the No?

    I don't really understand this equation:

    \frac{dN}{dt} = -\lambda N

    i know why it is negative [tex] \lambda N [/tex] as it's decreasing exponentially but what do the d and t stands for? Does the t stands for the half life? What is the use of the equation?

    Thanks a bunch!
  2. jcsd
  3. Jan 17, 2010 #2


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    Have you had calculus? d/dt is the time derivative.

  4. Jan 17, 2010 #3
    No.. i've not done calculus.

    so how do i solve for an equation involving [tex] \frac{dN}{dt} = -\lambda N[/tex]? What context do i use this equation?
  5. Jan 17, 2010 #4

    Doc Al

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    Last edited by a moderator: Apr 24, 2017
  6. Jan 17, 2010 #5


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    Just so you're aware of this (in case you aren't) that you're having a problem with the mathematics, not the physics. I'm pointing this out because, not just in your case, but as often the case, students just learning physics often think that physics is "difficult", when they are actually having issues with the mathematics.

    It's hard to teach you how to solve this when you haven't had calculus, because we will end up tell you how to solve it completely. I'm surprised that you can take this class without having had calculus as a prerequisite.

  7. Jan 17, 2010 #6
    dN/dt is the activity that is the number of decays in one second.Since radioactivity is a random process it may not be possible to get an exact equation for activity but lets make some assumptions:
    1.Assume that the activity is proportional to N,the number of atoms?For example two moles of U 235 as twice as active as one mol of U 235.
    2.Assume the activity depends on what the radioisotope is for example it seems likely that one mol of U 235 has a different activity to one mol of U 238.
    If the assumptions are reasonable we can write dN/dt=-lambda *N.When the equation is then tested experimentally it is shown that it works very well if N is large.(lambda=decay constant,a property of the isotope).When you think about it it makes sense,the activity depends on what the atoms are and how many there are.The rest is maths.
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