Answer:
0.002 mg of sample will be left after 40 days.
Step-by-step explanation:
Half life of the iodine-131 =[tex]t_{\frac{1}{2}}[/tex]= 8 days
Initial amount of iodine-131 =[tex]N_o[/tex]= 64 milligrams = 0.064 g
Amount of iodine-131 left after the time of 40 days = N
Decay constant =[tex]\lambda [/tex] = ?
[tex]\lambda =\frac{0.693}{t_{\frac{1}{2}}}=0.0866 day ^{-1}[/tex]
[tex]\log[N]=\log[N_o]-\frac{\lambda \times t}{2.303}[/tex]
[tex]\log[N]=\log[0.064 g]-\frac{0.0866 day^{-1}\times 40 days}{2.303}[/tex]
[tex]N=Antilog [-2.6979 g] [/tex]
N = 0.002004 g = 0.002 mg
0.002 mg of sample will be left after 40 days.
