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noboost4you
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After 3 days a sample of radon-222 decayed to 58% of its original amount:
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
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