Chapter 11, Problem 71AP

(a)

Interpretation Introduction

Interpretation:

Percentage of potassium-40 remaining after a decay of 3.6 billion years has to be calculated, considering the half-life of potassium-40 is 1.2 billion years.

Concept introduction:

As per the data given, the age of rocks and the other matter can be determined using several different radio tapes such as carbon − 14. When it comes to geosciences, potassium-40 is used to determine the age of rocks and it decays into argon-40 with a half-life of 1.2 years.

All radioactive reactions follow first order kinetics thus, the rate equation will be:

  

Here, k is rate constant, t is time taken by a reaction, is initial concentration of A and is concentration of reactant A at time t.

Also, the relation between rate constant and half-life time is:

  

(b)

Interpretation Introduction

Interpretation:

A reason should be provided to support the statement that uranium-238 is more useful for confirming the age than carbon-14.

Concept introduction:

As per the given data, the age of rocks and other matter can be determined using several different radio tapes like carbon − 14 and the half-life of uranium-238 is mentioned as 4.6 billion years.