Use the exponential decay model, A=Aoe^(kt), to solve this exercise. The half-life of polonium-210 is 140 days. How long will it take for a sample of this substance to decay to 20% of its original amount?

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Answer 1 · 2017-03-10T15:29:19

It will take #325.1#days

We use

#N(t)=N_0e^(-lambda t)#

#lambda# is the radioactive decay constant

#N(t)=0.2N_0#

#t_(1/2)# is the radioactive half life

#t_(1/2)=140d#

#lambda=ln2/t_(1/2)#

#=ln2/140=0.00495d^-1#

#0.2=e^(-0.00495t)#

#ln0.2=-0.00495t#

#t=ln0.2/-0.00495=325.1days#