Chapter 20, Problem 20.69QP

Interpretation Introduction

Interpretation:

• The fraction of Sodium-24 remains undecayed after 12.0h has to be determined.
• If the sample has $\text{6}\text{.0μg}$ of Sodium-24, amount of micrograms remains after 12h has to be determined.

Concept introduction:

• The decay constant (k) is independent of the quantity of radioactive material however depends only on the character of the nuclide.  Various nuclides have various decay constants.  The degree of radioactive decay depends on the decay constant and number of radioactive nuclei at specific time ( ${\text{N}}_{\text{t}}$).  The rate of decay is directly proportional to the number of radioactive nuclei in a given sample; it is expressed mathematically as,

${\text{Rate = kN}}_{\text{t}}$

• The decay constant used to define the quantity of radioactive material that remains after time period has gone.  The fraction of material that leftovers after a time period gas gone is the ratio of the number of radioactive nuclei ( ${\text{N}}_{\text{g}}$) in the real sample when the measurement happening.  This segment is frequently expressed as a percent.

The equation relating fraction of nuclei after a period of time has elapsed to the decay constant $\text{(ln}\frac{{\text{N}}_{\text{t}}}{{\text{N}}_{\text{g}}}\text{= -kt)}$