A wooden artifact from a Chinese temple has a 14C activity of 38.0 counts per minute as compared with an activity of 58.2 counts per minute for a standard of zero age. From the half-life for 14C decay, 5715 yr, determine the age of the artifact.

Question

Debbie Moore · Accepted Answer

The amount of time a substance has to take to reach half its starting concentration is known as the half-life of the reaction. It is symbolized by&amp;nbsp;t12&amp;nbsp;First order reaction governs every step of radioactive decay.The following is the equation for the first order reaction&#039;s half-life:t12=0.693k&amp;nbsp;where,&amp;nbsp;k = rate constant of first order reaction&amp;nbsp;Given value:&amp;nbsp;t12=5715&amp;nbsp;years&amp;nbsp;Plugging value in equation 1, we get:&amp;nbsp;k=0.6935715&amp;nbsp;k=1.21×10−4yr−1&amp;nbsp;The following is the first order reaction&#039;s integrated rate law expression:t=2.303klog⁡a(a−x)&amp;nbsp;where,&amp;nbsp;t = time period&amp;nbsp;(a-x) = Concentration of reactant remaining at time t = 38.0 counts per minute where a = starting concentration of the reactant = 58.2 counts per minutek = rate constant of first order reaction&amp;nbsp;=1.21×10−4yr−1&amp;nbsp;Plugging value in equation, we get:&amp;nbsp;t=2.3031.21×10−4yr−1log⁡58.238.0&amp;nbsp;t=3523.77yr

A wooden artifact from a Chinese temple has a 14C

Answered question

Answer & Explanation

New Questions in Other