Question

If you start with 3.0×10^10 I−131 atoms, how many are left after approximately 1month? I−131 has a half-life of 8.0 days. Express your answer using two significant figures.

Answer 1

For a first order reaction rate constant , k = ( 2.303 /t )x log ( M_o / M)

Where

M_o = initial number of atoms = 3.0x10¹⁰ atoms

M= Mass left after time t = ?

t = time = 1 month = 30 days

k = rate constant = 0.693/t_1/2                      t_1/2 = half life = 8.0 days

                          = 0.693 / 8.0 day^-1

                          = 0.087 day^-1

Plug the values we get

k = ( 2.303 /t )x log ( M_o / M)

log ( M_o / M) = (kt) /2.303

                   = 1.128

        M_o / M = 10^1.128

                  = 13.44

              M = M_o /13.44

                  = ( 3.0x10¹⁰ )/13.44

                 = 2.2x10⁹ atoms

The number of atoms left are 2.2x10⁹ atoms