Question

The half-life of radon-222 (Rn-222) is 3.823 days.How long would it take for three half-lives?

Answer 1

What is this… mortal kombat

Explanation:

Answer 2

Answer:
`7.949\ \text{days}`

Explanation:

Given

The half-life of a sample is
`T_{(1)/(2)}=3.823\ \text{days}`

Decay is given by

`A=A_o2^{\frac{-t}{T_{(1)/(2)}}}`

After 3 half-lives, one-eight of the sample is left

Insert the values

`\Rightarrow (A_o)/(8)=A_oe^{\frac{-t}{T_{(1)/(2)}}}\\\\\Rightarrow e^{\frac{t}{T_{(1)/(2)}}}=8\\\\\text{Taking log both sides}\\\Rightarrow \frac{t}{T_{(1)/(2)}}=\ln 8\\\\\Rightarrow t=3.823* \ln 8\\\\\Rightarrow t=7.944\ \text{days}`