Question

Iodine - 131 is used in medical imaging. Iodine - 131 has a half-life of 8days. How much Iodine - 131 remains in a patient's system after 1 month?

Answer 1

The nuclear reactions are of first order reactions .

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

Where

M_o = initial mass

M= Mass left after time t

t = time = 1 month = 30.4167 days

k = rate constant 0.693/t_1/2                  t_1/2 = half life = 8 days

   = 0.693 / 8

= 0.0866 day ^-1

Plug the values we get

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

                   = ( 0.0866x30.4167) / 2.303

                  = 1.144

M_o / M = 10^1.144

          = 13.9

    M = M_o / 13.9

       = 0.072 M_o

Therefore the mass of iodine -131 left in the patient is 0.072 times that of the initial mass