Chemistry: An Atoms First Approach

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



Chemistry: An Atoms First Approach

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

The decay constant is 0.0187billionyear-1_ .

Formula for the calculation of K is as follows



  •   t1/2 is the half life.

Substitute the value of t1/2 in the above equation


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

The equation depicting the radioactive decay process is


The given reaction is a first order reaction.

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


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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. The layer...Ch. 18 - Predict whether each of the following nuclides is...Ch. 18 - Each of the following isotopes has been used...Ch. 18 - The mass percent of carbon in a typical human is...Ch. 18 - At a flea market, youve found a very interesting...Ch. 18 - Define third-life in a similar way to half-life,...Ch. 18 - A proposed system for storing nuclear wastes...Ch. 18 - During World War II, tritium (3H) was a component...Ch. 18 - A positron and an electron can annihilate each...Ch. 18 - A small atomic bomb releases energy equivalent to...Ch. 18 - During the research that led to production of the...Ch. 18 - Using the kinetic molecular theory (see Section...Ch. 18 - Consider the following reaction, which can take...Ch. 18 - Photosynthesis in plants can be represented by the...Ch. 18 - Strontium-90 and radon-222 both pose serious...Ch. 18 - Complete the following table with the nuclear...Ch. 18 - A certain radioactive nuclide has a half-life of...Ch. 18 - Iodine-131 has a half-life of 8.0 days. 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