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Activity of substance after a certain time

  1. Oct 26, 2014 #1
    1. The problem statement, all variables and given/known data
    A sample consists of 2g of a radioactive element. The molar mass of the element is 67g. If the half life of the element is 78 hours, the activity of the sample after 48 hours is ?


    2. Relevant equations


    3. The attempt at a solution
    d(N)/dt = -λN
    (2/67 x 6.02x10^23) (ln 2 )/ (78x 3600) = 4.4x10^16s^-1
    A= acitivity
    A = A_0 (0.5)^x
    = (4.4x10^16) x (0.5)^(48/72)

    = 2.7x10^16s^-1

    but the ans given is 4.4x10^16s^-1
     
  2. jcsd
  3. Oct 26, 2014 #2

    haruspex

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    78, not 72.
     
  4. Oct 26, 2014 #3
    After changing 72 to 78.. Is my ans correct?
     
  5. Oct 26, 2014 #4

    haruspex

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    You posted that the answer given is 4.4x10^16s^-1, but that, as you showed, is the initial activity.
    With the 72 changed to 78 your working looks right to me.
     
  6. Oct 26, 2014 #5
    So the ans given is correct? Or my working is correct?
     
  7. Oct 26, 2014 #6

    haruspex

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    The answer given is clearly wrong because it is the initial activity. It must be less after 48 hours.
     
  8. Oct 27, 2014 #7
    the ans should be
    A = A_0 (0.5)^x
    = (4.4x10^16) x (0.5)^(48/78)
    = 2.87x10^16 ???
     
  9. Oct 27, 2014 #8

    haruspex

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    Looks right.
     
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