I need to find the isotope's half - life. Can I get some help please? Thanks!

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Answer 1 · 2017-12-23T12:35:41

By theory of radioactive disintegration of a sample of radio element we know

#N_t=N_0e^(-lambdat)#

Where

#N_0-># Initial number of radio element in the sample at #t=0#.

#N_t->#Number of radio element in the sample at after time t.

So #ln(N_t/N_0)=-lambdat#

Inserting the given data we have

#ln(5/80)=-lambda8#

#=>ln(2^-4)=-lambda8#

#=>-4ln(2)=-lambda8#

#=>ln(2)=2lambda.........(1)#

If #t_(1/2)# be half life period then at #t=t_(1/2)# we have

#N_(t_(1/2))/N_0=1/2#

So #ln(N_(t_(1/2))/N_0)=-lambdat_(1/2)#

#=>ln(1/2)=-lambdat_(1/2)#

#=>ln(2)=lambdat_(1/2).......(2)#

Comparing (1) and (2) we get

#t_(1/2=2)# hrs