Posted by **brittany** on Thursday, May 12, 2011 at 5:23pm.

If you accidentally spill phosphorus-32 onto your shoe, how long would it take before 99.9 of the radioactive material has decayed so that you can safely wear the shoes again?

- chemistry -
**DrBob222**, Thursday, May 12, 2011 at 5:33pm
Is that 99.9% or some other value? You have no units.

k = 0.693/t_{1/2}

Substitute and solve for k, then substitute k into the equation below.

ln(No/N) = kt

No = some convenient number like 100.

N will be 0.1 if 99.9% of the atoms have decayed.

k from above.

Solve for t (in the same units as the half life is given).

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