Answer:
Answer: 7.949\ \text{days}7.949 days
Step-by-step explanation:
Given
The half-life of a sample is T_{\frac{1}{2}}=3.823\ \text{days}T
2
1 =3.823 days
Decay is given by
A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}A=A
o
2
T
2
1
−t
After 3 half-lives, one-eight of the sample is left
Insert the values
\begin{gathered}\Rightarrow \dfrac{A_o}{8}=A_oe^{\dfrac{-t}{T_{\frac{1}{2}}}}\\\\\Rightarrow e^{\dfrac{t}{T_{\frac{1}{2}}}}=8\\\\\text{Taking log both sides}\\\Rightarrow \dfrac{t}{T_{\frac{1}{2}}}=\ln 8\\\\\Rightarrow t=3.823\times \ln 8\\\\\Rightarrow t=7.944\ \text{days}\end{gathered}
⇒
8
A
o
=A
o
e
T
2
1
−t
⇒e
T
2
1
t
=8
Taking log both sides
⇒
T
2
1
t
=ln8
⇒t=3.823×ln8
⇒t=7.944 days
