32 days
Further explanation
General formulas used in decay:
[tex]\large{\boxed{\bold{N_t=N_0(\dfrac{1}{2})^{t/t\frac{1}{2} }}}[/tex]
t = duration of decay
t 1/2 = half-life
N₀ = the number of initial radioactive atoms
Nt = the number of radioactive atoms left after decaying during T time
The half-life of iodine-131 is 8 days
No=80 g
Nt=5 g
[tex]\tt 5=80(\dfrac{1}{2})^{t/8}\\\\\dfrac{5}{80}=\dfrac{1}{2}^{t/8}\\\\\dfrac{1}{2}^4=\dfrac{1}{2}^{t/8}\\\\4=\dfrac{t}{8}\rightarrow 32~days[/tex]
