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

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 18, Problem 6Q
Textbook Problem
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## 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 of Solution

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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