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?

Answer 1

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).