The half-life of radon-222 (Rn-222) is 3.823 days.How long would it take for three half-lives?
2 answers:
Answer:
What is this… mortal kombat
Step-by-step explanation:
Answer: ![7.949\ \text{days}](https://tex.z-dn.net/?f=7.949%5C%20%5Ctext%7Bdays%7D)
Step-by-step explanation:
Given
The half-life of a sample is ![T_{\frac{1}{2}}=3.823\ \text{days}](https://tex.z-dn.net/?f=T_%7B%5Cfrac%7B1%7D%7B2%7D%7D%3D3.823%5C%20%5Ctext%7Bdays%7D)
Decay is given by
![A=A_o2^{\dfrac{-t}{T_{\frac{1}{2}}}}](https://tex.z-dn.net/?f=A%3DA_o2%5E%7B%5Cdfrac%7B-t%7D%7BT_%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7D)
After 3 half-lives, one-eight of the sample is left
Insert the values
![\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}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cdfrac%7BA_o%7D%7B8%7D%3DA_oe%5E%7B%5Cdfrac%7B-t%7D%7BT_%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7D%5C%5C%5C%5C%5CRightarrow%20e%5E%7B%5Cdfrac%7Bt%7D%7BT_%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%7D%3D8%5C%5C%5C%5C%5Ctext%7BTaking%20log%20both%20sides%7D%5C%5C%5CRightarrow%20%5Cdfrac%7Bt%7D%7BT_%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%3D%5Cln%208%5C%5C%5C%5C%5CRightarrow%20t%3D3.823%5Ctimes%20%5Cln%208%5C%5C%5C%5C%5CRightarrow%20t%3D7.944%5C%20%5Ctext%7Bdays%7D)
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Answer:
Step-by-step explanation:
Answer:
D.) 3
Step-by-step explanation:
x + 3 = 8
x - 3 = 2
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