After 3 days a sample of radon-222 decayed to 58% of its original amount:(adsbygoogle = window.adsbygoogle || []).push({});

a) what is the half-life of radon-222?

b) how long would it take the sample to decay to 10% of its original amount?

check my answers please:

a) m(t)=mo*e^kt

t = 3 and m(t)=.58mo

0.58mo = mo*e^3k

ln(.58) = 3k

k = -0.1816

1/2 = e^(-0.1816t)

ln(1/2)= -.1816t

t = 3.817 half life is approx 3.817 days

b) e^(-0.1816t) = .10

-0.1816t = ln(.10)

t = 12.68 it will take approx 12.68 days to reach 10%

the answer to (b) throws me. if half life is 3.817 days, 0% would be 7.634 days. where does this 12.68 days come from? i must be doing something wrong, unless (a) is wrong too.

thanks in advance

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# What is the half-life of radon-222?

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