Question

1. how long does it take for approximately 75% of carbon - 14 to decay into carbon - 12 (in thousands of years)? chapter 2: essential chemistry for biology

Explanation:

Step1: Recall half - life concept

The decay of carbon - 14 follows an exponential decay model. The half - life of carbon - 14 is approximately 5730 years. After one half - life, 50% of carbon - 14 decays. After a second half - life, half of the remaining 50% decays, so in total 75% decays.

Step2: Calculate time

Since it takes two half - lives for 75% of carbon - 14 to decay and the half - life of carbon - 14 ($t_{1/2}=5730$ years), the time $t = 2\times t_{1/2}$.
$t=2\times5730 = 11460$ years.

Answer:

11460 years