Answer to Question #271270 in General Chemistry for help

Question

Carbon12 (C12) is stable and is the most abundant isotope of carbon. An ancient scrap of paper has 0.7 times the Caron14 that a new piece of paper has. How many years old is the scrap of paper? (half-life of C14 is 5730 years)

Answer 1

Carbon dating yt =ln (C₁₄)₀ / (C₁₄)t

where (C₁₄)₀ is equivalent to amount of carbon 14 in new paper = 1

(C₁₄)t is amount of carbon 14 in an ancient scrpt of paper = 0.7

t = time of decay

y = decay constant

= Ln₂/t _1/2

Half life of carbon 14 = 5730

= Ln2/5730 years

Combining all values

(Ln2 x t)/5730 = Ln 1/0.7

t = 5730/Ln2 x Ln1/0.7

=4092.85 years

Answer= 4093 years