Question

a pure sample of a radioactive substance has 16*10^12 atoms and the half life is 3 minutes. How long does it take until 5*10^11 atoms of the substance have not yet decayed?

Answer 1

Given
  

   pure radio active substance initially N0 = 16*10^12 atoms are there

   half life time T1/2 = 3 min = 180 s

  

we know that T1/2 = 0.693/ Lambda LAmbda is decaay constant

   lambda = 0.693/180 = 0.00385 desintigrations per sec

   and the relation N = N0 e^(-Lambda*t)

  

           5*10^11 = 16*10^12*e^(-0.00385*t)

           t = 900.191 s
           t = 15 min