The nucleus of polonium Po(208,84) has a decay constant λ=0.239 years^-1. What is the half-life of Po(208,84) ? How many half-lives are there in 9 years? If a sample of Po contains 8000 atoms today, how many will remain after 9 years?

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Answer 1 · 2018-05-01T16:52:04

Please see the explanation below

The radioactive constant for Polonium (208.84) is

#lambda=0.239y^-1#

The half- life of Polonium (208.84) is

#t_(1/2)=ln2/lambda=ln2/0.239=2.9y#

In #9 y#, there are

#=9/2.9=3.1 "half lives"#

Initial number of atoms #N_0=8000 " atoms"#

The equation is

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

Therefore,

#N(9)=8000*e^(-0.239*9)=930.9 " atoms"#