   Chapter 19, Problem 6Q

Chapter
Section
Textbook Problem

# Scientists have estimated that the earth’s crust was formed 4.3 billion years ago. The radioactive nuclide 176Lu, which decays to 176Hf, was used to estimate this age. The half-life of 176Lu is 37 billion years. How are ratios of 176Lu to 176Hf utilized to date very old rocks?

Interpretation Introduction

Interpretation: Use of radioactive decay of 176Lu to 176Hf , estimate the formation of Earth’s crust 4.3 billion years ago is given. Utilization of ratio of 176Lu to 176Hf , date very old rocks is to be stated.

Concept introduction: Radioactive dating is an important method for determining the age of old rocks. It involves comparing the abundance ratio of a radioactive isotope with a reference isotope.

To determine: The decay constant, K and the ratio of 176Lu to 176Hf .

Explanation

The decay constant is 0.0187billionyear-1_ .

Formula for the calculation of K is as follows

K=0.693t1/2

Where,

•   t1/2 is the half life.

Substitute the value of t1/2 in the above equation

K=0.69337=0.0187billionyear-1_

The ratio of 176Lu to 176Hf is 1.53_ .

The equation depicting the radioactive decay process is

176Lu176Hf

The given reaction is a first order reaction.

The formula to calculate the time taken in a first order reaction is,

t=2

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