Chapter 20, Problem 20.29QP

Interpretation Introduction

Interpretation:

The activity of the carbon-14 in the bones in disintegration per minute per gram should be calculated.

Concept Introduction:

• Radioactive decay:
• This process is the accompanied by the emission of one or more than one types of ionizing radiation like alpha ,beta, neutron, particles and gamma rays are disintegrate
• Radio active life-it refers to the amount of time taken by completion of half of its original isotope to decay. The rate of decay is a fixed rate called half-life.
• Half-life used in carbon dating-technique for the age calculation of dead wood fossil, monument old tree etc.
• The half-life period s are determined by considering carbon dating technique.
• Carbon dating uses the half-life of carbon-14 to find the approximate age of an object. It’s may be 40.000 year old or younger.
• Radioactive isotope: An atom in a chemical compound is replaced by another atom, of the same chemical element. This is the principle behind the radioactive tracers.

  Titanium is the example of radioactive isotope.

To determine: The half-life period of the CARBON -14 in the bones calculated by using the given data.

Formula:

Half –life period:

${\text{t}}_{\text{1/2}}\text{=}\frac{\text{0}\text{.693}}{\text{k}}$

For identifying k or t value:

$\text{ln}\frac{{\text{N}}_{\text{t}}}{{\text{N}}_{\text{0}}}\text{=-kt}$

Given:

The age of animal’s bones determined by carbon C-14 dating to be $\text{8}{\text{.4×10}}^{\text{3}}\text{year}$ old.

The original activity was 15.3 dis/min per gram.