Chapter 20, Problem 79AP

Interpretation Introduction

Interpretation:

The percentage of $\text{C-14}$, originally present in the given sample, left after the given period of time is to be determined.

Concept introduction:

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

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

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 the percent of radioactive material left in the sample is calculated as follows:

$\text{Percent left = }\frac{\text{Amount of radioactive sample left after time t}}{\text{Initial amount of the Radioactive sample}}\times 100$

$\text{Percent left}=\frac{N_t}{N_o}\times 100$