Mathematics

Question

A certain radioactive isotope has a half-life of 11 days. If one is to make a table showing the half-life decay of a sample of this isotope from 32 grams to 1 gram; list the time (in days, starting with t = 0) in the first column and the mass remaining (in grams) in the second column, which type of sequence is used in the first column and which type of sequence is used in the second column?

1 Answer

  • If we choose to record measurements every 11 days, then the table is easy to produce:
    Days Mass
    0 32

    11 16
    22 8
    33 4
    44 2
    55 1


    To calculate remaining mass when days are NOT a multiple of 11, then we use the bottom formula in the attached graphic:
    Ending Amount = Beginning Amount / 2 ^ (elapsed time / half-life)
    So let's say after 1 day the remaining amount is
    Ending Amount = 32 / 2^(1/11) which equals
    30.045789 grams

    We can make a table for every ten days:

    Days    Mass
    0    32.00

    10 17.04

    20 9.07

    30 4.83
    40 2.57
    50 1.37

    60 0.73


    The sequence of the first column is an arithmetic sequence.
    The second column is an exponential decay sequence.



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