sample of 600 g of radioactive lead210 decays to polonium210

sample of 600 g of radioactive lead-210 decays to polonium-210 according to the function A(t) = 600 e^-0.032t, where t is time in years. Find the amount of radioactive lead remaining after 4 yr, 8 yr, 20 yr, Find the half-life. The amount of radioactive lead remaining after 4 yr will be The amount of radioactive lead remaining after 8 yr will be The amount of radioactive lead remaining after 20 yr will be The half-life is about

Solution

A(t) = 600e^(-0.032t)

a) after 4 yrs

t = 4: A(4) = 600e^(-0.032*4) = 600*0.879 = 527.40 = 527 gms

b) after t= 20yrs

A(2) = 600e^(-0.032*20) = 0.527*600 = 316.20 = 316 gms

c) Half life = 0.693/decay constant

= 0.693/0.032 = 21.66 years