Ashes from a campfire deep in a cave show carbon-14 activity of only one-eighth the activity of fresh wood. How long ago was that campfire made? Ans. (17190 years)



Data Given:


Activity of Carbon-14 from ashes = `\frac{1}{8^{th}}` of fresh wood

Half-life of Carbon-14 = T₁/₂ = 5730 s 


To Find:


Time taken = t = ?


Solution:

`\frac {1}{8^{th}}` show that it is 3rd half-lives (3 T₁/₂) of Carbon-14 elapsed. 

Therefore, using the formula

Time = Number of Half-lives ï½˜ half-life ( T₁/₂ )

Time = 3 ï½˜ T₁/₂ 

by putting values

Time = 3 ï½˜ 5730 years

Time = 17190 years   -----Ans
thus the campfire was made 17190 years ago.