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Radium-221 has a half-life of 30 seconds. How long will it take for 81% of a sample to decay?
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Radium-221 has a half-life of 30 seconds.
Mathematically, it mean M(t) = ,
where M(t) is the current remaining mass, is the initial mass, t is the time, in seconds.
They want you find the time when 81% of the initial uranium isotope will decay;
hence, 19%, or 0.19 of the initial mass remains.
For it, you write the decay equation in terms of half-life
0.19 = .
Take logarithm base 10 of both sides
log(0.19) = ,
t = = 71.9 seconds (rounded). ANSWER
Solved.
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