Question

The graph below shows the breakdown of radon-222.

Answer 1

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