Answer: 41.5 min
Step-by-step explanation:
This problem can be solved with the Radioactive Half Life Formula:
[tex]A=A_{o}.2^{\frac{-t}{h}}[/tex] (1)
Where:
[tex]A=22 g[/tex] is the final amount of the radioactive element
[tex]A_{o}=800 g[/tex] is the initial amount of the radioactive element
[tex]t[/tex] is the time elapsed
[tex]h=8 min[/tex] is the half life of the radioactive element
So, we need to substitute the given values and find [tex]t[/tex] from (1):
[tex]22 g=(800 g) 2^{\frac{-t}{8 min}}[/tex] (2)
[tex]\frac{22 g}{800 g}=2^{\frac{-t}{8 min}}[/tex] (3)
[tex]\frac{11}{400}=2^{\frac{-t}{8 min}}[/tex] (4)
Applying natural logarithm in both sides:
[tex]ln(\frac{11}{400})=ln(2^{\frac{-t}{8 min}})[/tex] (5)
[tex]-3.593=-\frac{t}{8 min}ln(2)[/tex] (6)
Clearing [tex]t[/tex]:
[tex]t=41.46 min \approx 41.5 min[/tex] This is the time elapsed
