You pick up a rock and measure that it has 400 parent atoms and 1200 daughter atoms. If the half life of the parent is 5000 years, how old is the rock?
Accepted Solution
A:
Answer:The rock is 6609.5 years oldStep-by-step explanation:Given :You pick up a rock and measure that it has 400 parent atoms and 1200 daughter atomsTo 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 remainingLet [tex]A_0[/tex] be the original amountSo. [tex]A=\frac{A_0}{2^n}[/tex][tex]\frac{A_0}{A}=2^n[/tex]We are given that it has 400 parent atomsSo, 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