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Gallium65, a radioactive isotope of gallium, decays by first order-kinetics. The half-life of this isotope is 15.2 min. How long would it take for 7/8 of a sample of this isotope to decay?

15.2 min
30.4 min
45.6 min
48.0 min

I'm not sure how to do this. I initially tried by finding k for the values given for the half life (ln2/15.2 min=k) and hten used k to find the value for when 7/8 was left over, but I keep getting t= 2.9 minutes which isn't right.

having trouble posting so I'm doing these in parts..

  • Chemistry -

    k = 0.692/15.2 min

    ln(No/N) = kt
    I would just put in 8 for No and 1 for N --which says 7/8 is gone leaving 1/8).
    ln(8/1) = kt and solve for t.

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