Question

Calculate the half life of a substance if you begin with 15 g and you have 0.23 g left after 10 days

Answer 1

Here initial quantity of substance N₀ = 15 gm

After 10 days, quantity N = 0.23 gm

   Time t = 10 days

We know    λ = 0.693/ t_1/2

                  λ = ( 2.303/ t )log( N₀/N)

therefore, 0.693/ t_1/2 = ( 2.303/ t )log( N₀/N)

Substituting all the values in above expression:

               0.693/ t_1/2 = ( 2.303/ 10)log( 15/0.23)

0.693/ t_1/2 = ( 2.303/ 10)log( 65.217391)

0.693/ t_1/2 = ( 2.303/ 10)* 1.8143634

0.693/ t_1/2    =    0.2303* 1.8143634

0.693/ t_1/2    =   0.41784

        Half life t_1/2    = 1.65849 days