Chapter 20, Problem 95AP

Interpretation Introduction

Interpretation:

The age of the given wood sample, with the help of given carbon-$14$ decay, is to be determined.

Concept introduction:

The amount of a particular radioactive isotope left, after time t, is given as

$\text{ln}\frac{N_t}{N_o}\text{=}-kt$

Here, $k$ is the rate constant for the radioactive decay, $N_t$ is the amount of it left after time $t$, and $N_0$ is the initial amount of the sample.

Nearly all the radioactive decay is of the first order and its rate constant is given as

$k\text{ = }\frac{0.693}{t_{1/2}}$

Here, $t_{1/2}$ is the half-life of the radioactive substance.

Half-life of the $\text{C-14}$ decay is $\text{5715 years}$.