CHEMISTRY HIGH SCHOOL

Please help I cant figure this outformula is m(t) = Mo e^-rt
decay rate is r= ln2/h. Radium-221 has a half-life of 30 seconds. How long will it take for 90% of a sample to decay = o-rt

Answers

Answer 1
Answer: half life formula is t1/2 = ln2/lambda
Where lambda is the decay constant
Rewriting we get lambda = ln2 / t1/2
Subbing in 30 seconds as half life we get lambda= 0.0231049 approx.
I assume only mass of radium is what you want.
Hence he have the formula
m=mo e^-lambda x t
Where m is mass after time
Mo is initial mass.
For 90% to decay, m/mo x100% = 90%
Hence m/mo = 0.1 this is because 90% has decays so we are left with 10%
Rearranging, m=mo e^-lambda x t
We obtain
(m/mo)=e^-lambda x t
Subbing in above values we get,
0.1=e^-0.0231049 x t
Take ln on both sides to get
ln(0.1) = -0.0231049 x t
Hence,
t = ln(0.1) / (-0.0231049)
t= 99.65787 s
It takes about 100 seconds for 90% to decay

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