It takes 11.4 days⇒three half-lives
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
t1/2=3.8 days
No=4.38 μg
Nt=0.55 μg
[tex]\tt 0.55=4.38\dfrac{1}{2}^{t/3.8}\\\\0.125=\dfrac{1}{2}^{t/3.8}\\\\\dfrac{1}{2}^3=\dfrac{1}{2}^{t/3.8}\\\\3=t/3.8\rightarrow t=3.8\times 3=11.4~days[/tex]
