Chapter 10, Problem 10B.9E

Interpretation Introduction

Interpretation:

The age of the carbon-14 present in the cloth has to be given.

Concept Introduction:

Radioactive Law:

The radioactive law states that the probability per unit time that a nucleus will decay is a constant independent of time.  This constant is called the decay constant and is denoted by $\text{k}$.  This constant probability may vary greatly between different types of nuclei, leading to the many different observed decay rates.  The radioactive decay of certain number of atoms (mass) is exponential in time.

  ${\text{N = N}}_{\text{0}}{\text{.e}}^{\text{-kt}}$

Where N is the number of radioactive nuclei remaining after time t.

N₀ is the number of radioactive nuclei in initial time.

k is the decay constant.

t is the time required to decay.

Half life period:

The half life is defined as the amount of time it takes for a given isotope to lose half of its radioactivity.

  ${\text{t}}_{\left(\text{1/2}\right)}\text{=}\frac{\text{ln2}}{\text{k}}$

Where k is the decay constant.