Chapter 21 Nuclear Chemistry

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Chapter 21Nuclear Chemistry
Chemistry, The Central Science, 10th
edition Theodore L. Brown H. Eugene LeMay, Jr.
and Bruce E. Bursten
John D. Bookstaver St. Charles Community
College St. Peters, MO ? 2006, Prentice Hall, Inc.
2
The Nucleus

• Remember that the nucleus is comprised of the two
  nucleons, protons and neutrons.
• The number of protons is the atomic number.
• The number of protons and neutrons together is
  effectively the mass of the atom.

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Isotopes

• Not all atoms of the same element have the same
  mass due to different numbers of neutrons in
  those atoms.
• There are three naturally occurring isotopes of
  uranium
• Uranium-233
• Uranium-235
• Uranium-238

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Radioactivity

• It is not uncommon for some nuclides of an
  element to be unstable, or radioactive.
• We refer to these as radionuclides.
• There are several ways radionuclides can decay
  into a different nuclide.

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Types ofRadioactive Decay
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Alpha Decay

• Loss of an ?-particle (a helium nucleus)

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Beta Decay

• Loss of a ?-particle (a high energy electron)

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Positron Emission

• Loss of a positron (a particle that has the same
  mass as but opposite charge than an electron)

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Gamma Emission

• Loss of a ?-ray (high-energy radiation that
  almost always accompanies the loss of a nuclear
  particle)

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Electron Capture (K-Capture)

• Addition of an electron to a proton in the
  nucleus
• As a result, a proton is transformed into a
  neutron.

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Measuring Radioactivity

• One can use a device like this Geiger counter to
  measure the amount of activity present in a
  radioactive sample.
• The ionizing radiation creates ions, which
  conduct a current that is detected by the
  instrument.

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SAMPLE EXERCISE 21.1 continued
PRACTICE EXERCISE Which element undergoes alpha
decay to form lead-208?
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PRACTICE EXERCISE Write a balanced nuclear
equation for the reaction in which oxygen-15
undergoes positron emission.
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Neutron-Proton Ratios

• Any element with more than one proton (i.e.,
  anything but hydrogen) will have repulsions
  between the protons in the nucleus.
• A strong nuclear force helps keep the nucleus
  from flying apart.

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Neutron-Proton Ratios

• Neutrons play a key role stabilizing the nucleus.
• Therefore, the ratio of neutrons to protons is an
  important factor.

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Neutron-Proton Ratios

• For smaller nuclei (Z ? 20) stable nuclei have a
  neutron-to-proton ratio close to 11.

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Neutron-Proton Ratios

• As nuclei get larger, it takes a greater number
  of neutrons to stabilize the nucleus.

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Stable Nuclei

• The shaded region in the figure shows what
  nuclides would be stable, the so-called belt of
  stability.

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Stable Nuclei

• Nuclei above this belt have too many neutrons.
• They tend to decay by emitting beta particles.

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Stable Nuclei

• Nuclei below the belt have too many protons.
• They tend to become more stable by positron
  emission or electron capture.

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Stable Nuclei

• There are no stable nuclei with an atomic number
  greater than 83.
• These nuclei tend to decay by alpha emission.

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Radioactive Series

• Large radioactive nuclei cannot stabilize by
  undergoing only one nuclear transformation.
• They undergo a series of decays until they form a
  stable nuclide (often a nuclide of lead).

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Some Trends

• Nuclei with 2, 8, 20, 28, 50, or 82 protons or
  2, 8, 20, 28, 50, 82, or 126 neutrons tend to be
  more stable than nuclides with a different number
  of nucleons.

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Some Trends

• Nuclei with an even number of protons and
  neutrons tend to be more stable than nuclides
  that have odd numbers of these nucleons.

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SAMPLE EXERCISE 21.4 Predicting Nuclear Stability
Solution   Analyze We are asked to identify
especially stable nuclei, given their mass
numbers and atomic numbers. Plan We look to see
whether the numbers of protons and neutrons
correspond to magic numbers.
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PRACTICE EXERCISE Predict the mode of decay of
(a) plutonium-239, (b) indium-120.
Answer (a) ? decay, (b) ? decay
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Nuclear Transformations

• Nuclear transformations can be induced by
  accelerating a particle and colliding it with the
  nuclide.

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Particle Accelerators

• These particle accelerators are enormous, having
  circular tracks with radii that are miles long.

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Kinetics of Radioactive Decay

• Nuclear transmutation is a first-order process.
• The kinetics of such a process, you will recall,
  obey this equation

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Kinetics of Radioactive Decay

• The half-life of such a process is

• Comparing the amount of a radioactive nuclide
  present at a given point in time with the amount
  normally present, one can find the age of an
  object.

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Kinetics of Radioactive Decay
A wooden object from an archeological site is
subjected to radiocarbon dating. The activity of
the sample that is due to 14C is measured to be
11.6 disintegrations per second. The activity of
a carbon sample of equal mass from fresh wood is
15.2 disintegrations per second. The half-life
of 14C is 5715 yr. What is the age of the
archeological sample?

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Kinetics of Radioactive Decay

• First we need to determine the rate constant,
  k, for the process.

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Kinetics of Radioactive Decay

• Now we can determine t

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SAMPLE EXERCISE 21.7 Calculating the Age of a
Mineral
A rock contains 0.257 mg of lead-206 for every
milligram of uranium-238. The half-life for the
decay of uranium-238 to lead-206 is 4.5 ? 109 yr.
How old is the rock?
Solution   Analyze Were told that a rock
sample has a certain amount of lead-206 for every
unit weight of uranium-238 and asked to estimate
the age of the rock. Plan Presumably the
lead-206 is due entirely to radioactive decay of
uranium-228 to form lead-206, with a known
half-life. To apply first-order kinetics
expressions (Equations 21.19 and 21.20) to
calculate the time elapsed since the rock was
formed, we need first to calculate how much
initial uranium-238 there was for every 1
milligram that remains today.
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SAMPLE EXERCISE 21.7 continued
PRACTICE EXERCISE A wooden object from an
archeological site is subjected to radiocarbon
dating. The activity of the sample that is due to
14C is measured to be 11.6 disintegrations per
second. The activity of a carbon sample of equal
mass from fresh wood is 15.2 disintegrations per
second. The half-life of 14C is 5715 yr. What is
the age of the archeological sample?
Answer 2230 yr
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SAMPLE EXERCISE 21.8 Calculations Involving
Radioactive Decay
If we start with 1.000 g of strontium-90, 0.953 g
will remain after 2.00 yr. (a) What is the
half-life of strontium-90? (b) How much
strontium-90 will remain after 5.00 yr? (c) What
is the initial activity of the sample in Bq and
in Ci?
Solution   (a) Analyze We are asked to
calculate a half-life, t1/2, based on data that
tell us how much of a radioactive nucleus has
decayed in a given period of time and (N0 1.000
g, Nt 0.953 g, and t 2.00 yr). Plan We first
calculate the rate constant for the decay, k,
then use that to compute t1/2.
(b) Analyze We are asked to calculate the amount
of a radionuclide remaining after a given period
of time. Plan We need to calculate the amount of
strontium at time t, Nt , using the initial
quantity, N0 , and the rate constant for decay,
k, calculated in part (a).
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SAMPLE EXERCISE 21.8 continued
(c) Analyze We are asked to calculate the
activity of the sample in becquerels and
curies. Plan We must calculate the number of
disintegrations per second per atom, then
multiply by the number of atoms in the sample.
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SAMPLE EXERCISE 21.8 continued Bq 1
disintegration/sec Ci 3.7 x 1010
disintegration/sec
We have used only two significant figures in
products of these calculations because we dont
know the atomic weight of 90S to more than two
significant figures without looking it up in a
special source.
PRACTICE EXERCISE A sample to be used for medical
imaging is labeled with 18F, which has a
half-life of 110 min. What percentage of the
original activity in the sample remains after 300
min?
Answer 15.1
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SAMPLE EXERCISE 21.9 Calculating Mass Change in a
Nuclear Reaction
Solution Analyze We are asked to calculate the
energy change in a nuclear reaction. Plan We
must first calculate the mass change in the
process. We are given atomic masses, but we need
the masses of the nuclei in the reaction. We
calculate these by taking account of the masses
of the electrons that contribute to the atomic
masses.
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SAMPLE EXERCISE 21.9 continued
Answer 3.19 ? 103g
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Energy in Nuclear Reactions

• There is a tremendous amount of energy stored in
  nuclei.
• Einsteins famous equation, E mc2, relates
  directly to the calculation of this energy.

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Energy in Nuclear Reactions

• In the types of chemical reactions we have
  encountered previously, the amount of mass
  converted to energy has been minimal.
• However, these energies are many thousands of
  times greater in nuclear reactions.

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Energy in Nuclear Reactions

• For example, the mass change for the decay of 1
  mol of uranium-238 is -0.0046 g.
• The change in energy, ?E, is then
• ?E (?m) c2
• ?E (-4.6 ? 10-6 kg)(3.00 ? 108 m/s)2
• ?E -4.1 ? 1011 J

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Nuclear Fission

• How does one tap all that energy?
• Nuclear fission is the type of reaction carried
  out in nuclear reactors.

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Nuclear Fission

• Bombardment of the radioactive nuclide with a
  neutron starts the process.
• Neutrons released in the transmutation strike
  other nuclei, causing their decay and the
  production of more neutrons.

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Nuclear Fission

• This process continues in what we call a nuclear
  chain reaction.

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Nuclear Fission

• If there are not enough radioactive nuclides in
  the path of the ejected neutrons, the chain
  reaction will die out.

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Nuclear Fission

• Therefore, there must be a certain minimum
  amount of fissionable material present for the
  chain reaction to be sustained Critical Mass.

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Nuclear Reactors

• In nuclear reactors the heat generated by the
  reaction is used to produce steam that turns a
  turbine connected to a generator.

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Nuclear Reactors

• The reaction is kept in check by the use of
  control rods.
• These block the paths of some neutrons, keeping
  the system from reaching a dangerous
  supercritical mass.

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Nuclear Fusion

• Fusion would be a superior method of generating
  power.
• The good news is that the products of the
  reaction are not radioactive.
• The bad news is that in order to achieve fusion,
  the material must be in the plasma state at
  several million kelvins.

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Nuclear Fusion

• Tokamak apparati like the one shown at the right
  show promise for carrying out these reactions.
• They use magnetic fields to heat the material.

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SAMPLE EXERCISE 21.10 Writing Nuclear Equations
Write the nuclear equations for the formation of
239Pu from 238U.
Solution   Analyze We are asked to write the
nuclear equations for the nuclear reactions
leading to formation of 239Pu from 238U. Plan
We know from the previous discussion that the
formation of 239Pu from 238U involves absorption
of a neutron by 238U, followed by two successive
beta emissions.
Comment We can check our equations for balance
in both charge and mass.
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SAMPLE INTEGRATIVE EXERCISE Putting Concepts
Together
Potassium ion is present in foods as KCl and is
an essential nutrient in the human body. One of
the naturally occurring isotopes of potassium,
potassium-40, is radioactive. Potassium-40 has a
natural abundance of 0.0117 and a half-life of
t1/2 1.28 ? 109 yr. It undergoes radioactive
decay in three ways 98.2 is by electron
capture, 1.35 is by beta emission, and 0.49 is
by positron emission. (a) Why should we expect
40K to be radioactive? (b) Write the nuclear
equations for the three modes by which 40K
decays. (c) How many 40K ions are present in
1.00 g of KCl? (d) How long does it take for
1.00 of the 40K in a sample to undergo
radioactive decay?
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SAMPLE INTEGRATIVE EXERCISE continued
That is, it would take 18.6 million years for
just 1.00 of the 40K in a sample to decay.