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Decay Constant?

  1. Mar 26, 2014 #1
    1. The problem statement, all variables and given/known data
    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 resulting from the decay are absorbed, and all that exit on the film side of the copper sheet are counted. Immediately after preparation, the counter registers 7340 alpha particles per second.

    A)What is the decay constant of Th(A=228, Z=90)?

    B)How much thorium has been electroplated onto the copper?

    2. Relevant equations

    At=Ao*e^[-λ*t]
    λ=0.693/T


    3. The attempt at a solution

    A)
    T=1.913y

    λ=(0.693/1.913)
    λ= 0.181 y^-1

    This is incorrect.
    Any guidance or hints would be appreciated!
     
  2. jcsd
  3. Mar 26, 2014 #2

    Simon Bridge

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    Cannot see your reasoning.
    i.e. what proportion of the alphas emitted are counted?
     
  4. Mar 27, 2014 #3

    SteamKing

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    You must also be using the correct units. The half-life of Th-228 is measured in years and you have an alpha count in particles per second.
     
  5. Mar 27, 2014 #4
    I got the first part A)
    T=1.913y = 6.037e7 sec

    λ=(0.693/6.037e7)
    λ=1.15e-8 s^-1

    but I have no idea where to start with part b. Any suggestions?
     
  6. Mar 27, 2014 #5

    Simon Bridge

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    How is the decay rate related to the amount of substance present?
     
  7. Mar 27, 2014 #6
    I'm not sure. I feel like I'm missing a formula
     
  8. Mar 27, 2014 #7

    Simon Bridge

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    You listed two formulas in post #1 and used only one of them.
     
  9. Mar 27, 2014 #8
    I was thinking:
    At=Ao*e^[-λ*t]
    Ao=7340 particles/sec
    λ=1.15e-8 s^-1

    But that leaves me with two unknowns.
    I'm assuming I need to find At, to relate it to the amount electroplated onto the copper, but dont have t.

    Still stuck :(
     
  10. Mar 27, 2014 #9

    Simon Bridge

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    When you use formulas you have to realize what they are for, what they mean.

    You mean you don't know t and A(t)?
    Consider: the problem statement says "immediately after preparation".
    What time is that?

    So you reckon A(t) is the decay rate at time t?
    In which case you need to relate A0 to the initial number of particles present.

    Hint: the decay rate is R=-dN/dt and is directly proportional to the number of particles present.
     
  11. Mar 28, 2014 #10
    This equation may be helpful for your question:

    [itex]R = \frac{0.693N}{t1/2}[/itex]

    R = activity, rate of decay
    N = number of particles
    t1/2 = half-life
     
    Last edited: Mar 28, 2014
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