Radiocarbon dating is effective on specimens up to 40000 yea

Radiocarbon dating is effective on specimens up to 40,000 years old. In 1951, a nuclear chemist was trying to determine the age of some scrollsthat were recently found. Carbon-14 has a half-life of 5730 years. If he found 9.3% of the original carbon-14 still present, in about what year were the scrolls made. The scrolls were mad in about A.D _____. (They\'re like a smalll A.D number usually) please help


Also do not please post a 19,000.56 number. I need the number in A.D

Solution

Use the half-life decay equation:

C = 2^ (-t/hl)

C is current percent concentration of Carbon-14, I is the initial concentration, t is the age in years, and hl is the half-life of Carbon-14 in years.

0.093 = 2 ^ (-t/5730)

take the logarithm of both sides:

log (0.093) = (-t/5730) * log (2)

-2.375 = -t/5730

t = 13608 years.