Carbon-14 has a half-life of 5730 years. How long will it take for the quantity of carbon-14 in a sample to drop to one-eighth of the initial quantity? Ans. (1.72 ｘ 10⁴ years).



Data Given:


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

Remaining Original Fraction of C-14 = `\frac{1}{8^{th}}`


To Find:



Time taken during dropping of C-14 to `\frac{1}{8^{th}}` = ?


Solution:

The quantity of C-14 drop to `\frac{1}{8^{th}}` of the original quantity after Three Half-lives (3 T₁/₂ ). Hence, 

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 

Time = 1.72 ï½˜ 10⁴ years -----------Ans.