An isotope has a half life of 90 days. How many days will it take for a 5 mg sample to decay to 1 mg?

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Answer 1 · 2017-06-08T19:23:51

The number of days is #=209days#

The radioactive decay is represented by the equation

#M(t)=M(0)e^(-lambdat)#

The radioactive constant is

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

Here, the half life is

#t_(1/2)=90d#

#lambda=ln2/90=7.7*10^-3#

The initial mass is #M(0)=5mg#

The final mass is #m(t)=1mg#

#1=5e^(-7.710^(-3)t)#

#e^(-7.710^-3)t=1/5=0.2#

#-7.710^-3t=ln0.2=-1.609#

#t=1.609/7.710^-3#

#=209d#