A radioisotope P has a half-life of 3 s. At t = 0, a given sample of this isotope contains 8000 atoms. Calculate (i) its decay constant, (ii) average life, (iii) the time t1 when 1000 atoms of the isotope P remain in the sample, and (iv) number of decays per second in the sample at t = t1 s.

2 answers

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I looked through this list of questions. They are cookbook questions and the recipes are in the student's text.
for example if we know a half life in seconds and it is exponential decay
then amount = original amount *e^-kt
if amount/original amount = 1/2
then
1/2 = e^-kT where T is the half life
ln .5 = - k T
so
k = -ln .5 / T