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Chemistry: An Atoms First Approach

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

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BuyFindarrow_forward

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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Chapter 18 Solutions

Chemistry: An Atoms First Approach
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Ch. 18 - When nuclei undergo nuclear transformations, rays...Ch. 18 - There is a trend in the United States toward using...Ch. 18 - Which type of radioactive decay has the net effect...Ch. 18 - Consider the following graph of binding energy per...Ch. 18 - What are transuranium elements and how are they...Ch. 18 - Scientists have estimated that the earths crust...Ch. 18 - Why are the observed energy changes for nuclear...Ch. 18 - Natural uranium is mostly nonfissionable 238U; it...Ch. 18 - Much of the research on controlled fusion focuses...Ch. 18 - A recent study concluded that any amount of...Ch. 18 - Write an equation describing the radioactive decay...Ch. 18 - In each of the following radioactive decay...Ch. 18 - Supply the missing particle, and state the type of...Ch. 18 - Write balanced equations for each of the processes...Ch. 18 - Write an equation describing Ute radioactive decay...Ch. 18 - In each of the following radioactive decay...Ch. 18 - Uranium-235 undergoes a series of -particle and,...Ch. 18 - The radioactive isotope 247Bk decays by a series...Ch. 18 - One type of commercial smoke detector contains a...Ch. 18 - Thorium-232 is known to undergo a progressive...Ch. 18 - There are four stable isotopes of iron with mass...Ch. 18 - The only stable isotope of fluorine is...Ch. 18 - In 1994 it was proposed (and eventually accepted)...Ch. 18 - Many elements have been synthesized by bombarding...Ch. 18 - The rate constant for a certain radioactive...Ch. 18 - Americium-241 is widely used in smoke detectors....Ch. 18 - Krypton consists of several radioactive isotopes,...Ch. 18 - Radioactive copper-64 decays with a half-life of...Ch. 18 - A chemist wishing to do an experiment requiring...Ch. 18 - The curie (Ci) is a commonly used unit for...Ch. 18 - The first atomic explosion was detonated in the...Ch. 18 - Iodine-131 is used in the diagnosis and treatment...Ch. 18 - Technetium-99 has been used as a radiographic...Ch. 18 - Phosphorus-32 is a commonly used radioactive...Ch. 18 - The bromine-82 nucleus has a half-life of 1.0 103...Ch. 18 - Fresh rainwater or surface water contains enough...Ch. 18 - A living plant contains approximately the same...Ch. 18 - Assume a constant 14C/12C ratio of 13.6 counts per...Ch. 18 - A rock contains 0.688 mg 206Pb for every 1.000 mg...Ch. 18 - The mass ratios of 40Ar to 40K also can be used to...Ch. 18 - The sun radiates 3.9 1023 J of energy into space...Ch. 18 - The earth receives 1.8 1014 kJ/s of solar energy....Ch. 18 - Many transuranium elements, such as plutonium-232,...Ch. 18 - The most stable nucleus in terms of binding energy...Ch. 18 - Calculate the binding energy in J/nucleon for...Ch. 18 - Calculate the binding energy per nucleon for H12...Ch. 18 - The mass defect for a lithium-6 nucleus is 0.03434...Ch. 18 - The binding energy per nucleon for magnesium-27 is...Ch. 18 - Calculate the amount of energy released per gram...Ch. 18 - The easiest fusion reaction to initiate is...Ch. 18 - The typical response of a Geiger-Mller tube is...Ch. 18 - When using a Geiger-Mller counter to measure...Ch. 18 - Consider the following reaction to produce methyl...Ch. 18 - A chemist studied the reaction mechanism for the...Ch. 18 - Uranium-235 undergoes many different fission...Ch. 18 - Breeder reactors are used to convert the...Ch. 18 - Which do you think would be the greater health...Ch. 18 - Consider the following information: i. 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