Respuesta :
Answer:
The rock is 6609.5 years old
Step-by-step explanation:
Given :You pick up a rock and measure that it has 400 parent atoms and 1200 daughter atoms
To Find :If the half life of the parent is 5000 years, how old is the rock?
Solution:
Formula : [tex]\text{Amount remaining}=\frac{\text{original amount}}{2^n}[/tex]
Let A be the amount remaining
Let [tex]A_0[/tex] be the original amount
So. [tex]A=\frac{A_0}{2^n}[/tex]
[tex]\frac{A_0}{A}=2^n[/tex]
We are given that it has 400 parent atoms
So, if there were 1000 atoms originally then 400 are remaining
[tex]\frac{1000}{400}=2^n[/tex]
[tex]\frac{5}{2}=2^n[/tex]
[tex]\log(\frac{5}{2})=n\log 2[/tex]
[tex]\frac{\log(\frac{5}{2})}{\log 2}=n[/tex]
[tex]1.3219=n[/tex]
So, t = [tex]t_{\frac{1}{2}}\times 1.3219[/tex]
t = [tex]5000\times 1.3219[/tex]
t = [tex]6609.5[/tex]
Hence the rock is 6609.5 years old
Answer:
10,000 years.
Step-by-step explanation:
∵ Number of parent atoms = 400,
Number of daughter atoms = 1200,
So, the proportional of parent atoms = [tex]\frac{400}{1200}[/tex] = 0.25 = 25 %
Since, 25% proportion of parent atoms shows there are two half lifes,
Given,
The number of years in one half life = 5000,
Hence, the age of the rock = 2 × 5000 = 10,000 years.
