Question

A potassium isotope has a half-life of 1.25 billion years. Given that scientists estimate Earth's age to be 4.6 billion years, what is the most likely percentage of parent to daughter isotopes of this element currently existing on Earth?
A. Less than 10 percent
B. 25 percent
C. 50 percent
D. More than 75 percent

Answer 1

A. Less than 10 percent

Answer 2

Answer:

Option D

Explanation:

The exponential equation to determine the age of any radioactive object is as follows -

$t = [\frac{ln\frac{N}{N_{0} } }{-0.693} ]* t_{\frac{1}{2} }$

where

$N =$ Final quantity of isotope after degradation

$N_{0} =$ initial quantity of isotope

$t_{\frac{1}{2} } =$ half life period of isotope

$t =$ time period of degradation

Substituting the given values in above equation we get -

$4.6 = [\frac{ln\frac{N}{N_{0} } }{-0.693} ]* 1.25\\ln\frac{N}{N_{0}} = 2.550\\\frac{N}{N_{0}} = 12.81$

$\frac{N_{0}}{N} = \frac{1}{12.81} \\0.07$

Remaining isotope

$= 1 -0.07\\= 0.93$

Hence, option D is correct.