Question

A sealed container has 15 μg of radon-222.

A)What's the sample's activity?​

B)Find the activity of radon remaining after 23 days.

C)Find the amount of radon remaining after 23 days.

Answer 1

Initial    mass m₀ = 15*10^-6 ,

half life of radon   T_1/2   = 3.8 days

Initial number of atoms N₀   = m₀ N_A / M    ...............(1)

M =   222 g /mole

plug all values in (1) we get  

N₀   = 4.06*10¹⁶ atoms

          decay constant   λ =   0.693 / T_1/2     =   ( 0.693 /3.8 days) ( day / 24*60*60 sec )

                                       =   2.11*10^-6   / sec

   (a) activity    A = λ N₀    =  ( 2.11*10^-6    / sec )( 4.06*10¹⁶ atoms )  

                                           = 8.567 * 10¹⁰   decay /sec

                                           =  ( 8.567* 10¹⁰   Bq ) ( Ci / 3.7*10¹⁰ Bq)   = 2.32 Ci

(b)    A = A₀ e^-λt    .................(2)

       Here    A₀    = 8.568* 10¹⁰   Bq   , t = 23 days ,

      λ =   0.693 / T_1/2    , T_1/2       =  3.8 days   

   plug all values in (2) we get

          A   after   23 days   = 10.28 * 10¹⁰   Bq

                                        =   (10.28* 10¹⁰   Bq ) (  ( Ci / 3.7*10¹⁰ Bq) = 2.77 Ci

(c)   mass m = m₀ e^-λt   ................(3)

     Here     λ =   0.693 / T_1/2    , T_1/2       =  3.8 days   ,t = 23 days

m₀ = 15*10^-6 g

plug all values in (3)   we get

           mass after 23 days   m = 0.154*10^-6 g