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Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097

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BuyFindarrow_forward

Chemistry

9th Edition
Steven S. Zumdahl
ISBN: 9781133611097
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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