An archaeologist has found a fossil in which the ratio of ${ } ^ { 14 } \mathrm { C }$ to ${ } ^ { 12 } \mathrm { C }$ is $\frac { 1 } { 5 }$ the ratio in the atmosphere. Approximately how old is the fossil? The half-life of ${ } ^ { 14 } \mathrm { C }$ is 5,730 years. Round to the nearest whole year.
A) 14,325 years
B) 13,305 years
C) 28,650 years
D) 13,335 years

Question

Quizplus · Accepted Answer

The age of the fossil can be calculated using the formula for radioactive decay: $ t = \frac{\ln(N_0/N)}{\lambda} $, where $ \lambda = \frac{\ln(2)}{\text{half-life}} $. Given that the ratio is $ \frac{1}{5} $, $ N_0/N = 5 $. Using the half-life of 5,730 years, the calculation gives approximately 13,305 years.

An Archaeologist Has Found a Fossil in Which the Ratio 14C{ } ^ { 14 } \mathrm { C }14C

An Archaeologist Has Found a Fossil in Which the Ratio ${ } ^ { 14 } \mathrm { C }$