Chapter 18, Problem 40QAP

Interpretation Introduction

Interpretation:

The age of a Scotch whiskey sample having 62% tritium content that of the water in the area should be estimated.

Concept introduction:

Activity is defined as the product of rate constant and number of atoms. It is also defined as the rate of decay or expresses number of atoms decays in unit time.

The mathematical expression is given by:

$\text{A = kN}$

Where, A = activity, k = first order rate constant and N = number of radioactive nuclei.

Activity can be expressed in following units:

1 Bq = 1 atom/s

1 Ci = 3.700 × 10¹⁰ atoms/s

The relation between half-life and first order rate constant is given by:

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

Where, k = first order rate constant and ${\text{t}}_{\text{1/2}}$ = half-life

The activity of sample is directly proportional to the amount of C-14. The mathematical expression is given by:

$\ln \frac{A_o}{A}=kt$

Where, $A_o$ = original activity

$A$ = measured activity

t= age of the sample