Chapter 21 Nuclear Chemistry © 2012 Pearson Education, Inc.

Chapter 21

Nuclear Chemistry

© 2012 Pearson Education, Inc.

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The Nucleus

• Remember that the nucleus is composed 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 atomic mass.

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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, for example, three naturally occurring isotopes of uranium:– Uranium-234– 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

Alpha decay is the loss of an α-particle (a helium nucleus):

He42

U23892

Th23490 He4

2 +

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Sample Exercise 21.1 Predicting the Product of a Nuclear Reaction

What product is formed when radium-226 undergoes alpha decay?

Practice ExerciseWhich element undergoes alpha decay to form lead-208?

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A. +2B. –2C. +4D. –4

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Beta Decay

Beta decay is the loss of a -particle (a high-energy electron):

01 e0

1or

I13153 Xe131

54 + e0

1

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Electron Capture (K-Capture)

Addition of an electron to a proton in the nucleus is known as electron capture or K-capture.– The result of this process is that a proton is

transformed into a neutron:

p11 + e0

1 n10

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Positron Emission

Some nuclei decay by emitting a positron, a particle that has the same mass as, but an opposite charge to, that of an electron:

e01

C116

B115 + e0

1

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Gamma Emission

Gamma emission is the loss of a -ray, which is high-energy radiation that almost always accompanies the loss of a nuclear particle:

00

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Sample Exercise 21.2 Writing Nuclear Equations

Write nuclear equations for (a) mercury-201 undergoing electron capture; (b) thorium-231 decaying to protactinium-231.

Practice ExerciseWrite a balanced nuclear equation for the reaction in which oxygen-15 undergoes positron emission.

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A. Alpha particleB. NeutronC. ProtonD. Beta particle

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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.

• Neutrons play a key role stabilizing the nucleus.

• Therefore, the ratio of neutrons to protons is an important factor.

• For smaller nuclei (Z 20), stable nuclei have a neutron-to-proton ratio close to 1:1.

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

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Stable Nuclei

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

• Nuclei above this belt have too many neutrons.

• These nuclei tend to decay by emitting beta particles.

• Nuclei below the belt have too many protons.

• Nuclei 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.

• Nuclei with such large atomic numbers tend to decay by alpha emission.

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Sample Exercise 21.3 Predicting Modes of Nuclear Decay

Predict the mode of decay of (a) carbon-14, (b) xenon-118.

Practice ExercisePredict the mode of decay of (a) plutonium-239, (b) indium-120.

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A. 82 neutronsB. 92 neutronsC. 102 neutronsD. 112 neutrons

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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.

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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A. Even number of protons and fewer than three stable isotopes, 2 elements; odd number of protons and more than two isotopes, 2 elements

B. Even number of protons and fewer than three stable isotopes, 1 element; odd number of protons and more than two isotopes, 3 elements

C. Even number of protons and fewer than three stable isotopes, 4 elements; odd number of protons and more than two isotopes, 1 element

D. Even number of protons and fewer than three stable isotopes, 3 elements; odd number of protons and more than two isotopes, 0 elements

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A. All have an even number of neutrons.B. All have an odd number of neutrons.C. F and Na have an odd number of neutrons whereas Al and P have

an even numberD. F and P have an odd number of neutrons whereas Al and Na have

an even number.

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Sample Exercise 21.4 Predicting Nuclear Stability

Predict which of these nuclei are especially stable: , , .

Practice ExerciseWhich of the following nuclei would you expect to exhibit a special stability: , , ?

.

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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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Sample Exercise 21.5 Writing a Balanced Nuclear Equation

Write the balanced nuclear equation for the process summarized as .

Practice ExerciseWrite the condensed version of the nuclear reaction

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A. Yes, because a neutron has mass and can interact with an electrostatic or magnetic field and is accelerated by an electrostatic or magnetic field.

B. No, because a neutron has no charge and therefore cannot be accelerated by an electrostatic or magnetic field.

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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:

= −kt Nt

N0

ln

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Kinetics of Radioactive Decay

• The half-life of such a process is

= t1/2 0.693

k

• 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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A. 25.0 gB. 12.5 gC. 6.25 gD. 3.13 g

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Practice ExerciseCarbon-11, used in medical imaging, has a half-life of 20.4 min. The carbon-11 nuclides are formed, and the carbon atoms are then incorporated into an appropriate compound. The resulting sample is injected into a patient, and the medical image is obtained. If the entire process takes five half-lives, what percentage of the original carbon-11 remains at this time?

Sample Exercise 21.6 Calculation Involving Half-Lives

The half-life of cobalt-60 is 5.3 yr. How much of a 1.000-mg sample of cobalt-60 is left after 15.9 yr?

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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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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:

= t1/2 0.693

k

= 5715 yr 0.693

k

= k 0.693

5715 yr

= k 1.21 104 yr1© 2012 Pearson Education, Inc.

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Kinetics of Radioactive Decay

Now we can determine t:

= −kt Nt

N0

ln

= −(1.21 104 yr1)t 11.615.2

ln

= −(1.21 104 yr1)t ln 0.763

= t 2240 yr

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A. Spontaneous radioactive processes have differing reaction mechanisms that do not fit a zero-order or second-order kinetic process.

B. Spontaneous radioactive processes have differing reaction rates that do not fit a zero-order or second-order kinetic process.

C. Spontaneous radioactive processes are either unimolecular or trimolecular processes leading to a first-order or third-order kinetic process.

D. Spontaneous radioactive processes are unimolecular processes leading only to a first-order kinetic process.

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A. (a) Yes (see equation 21.18)(b) No (see equation 21.20)

B. (a) No (see equation 21.18)(b) Yes (see equation 21.20)

C. (a) No (see equation 21.18)(b) No (see equation 21.20)

D. (a) Yes (see equation 21.18)(b) Yes (see equation 21.20)

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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?

Sample Exercise 21.7 Calculating the Age of a Mineral

Practice ExerciseA wooden object from an archeological site is subjected to radiocarbon dating. The activity 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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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 becquerels and curies?

Sample Exercise 21.8 Calculations Involving Radioactive Decay

Practice ExerciseA 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?

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A. YesB. No. Alpha and beta particles will pass through

matter with equal efficiency but not gamma raysC. No. Alpha particles and gamma rays will pass

through matter with equal efficiency but not beta particles.

D. No. Alpha particles are more readily absorbed by matter than beta particles and gamma rays.

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Energy in Nuclear Reactions

• There is a tremendous amount of energy stored in nuclei.

• Einstein’s famous equation, E = mc2, relates directly to the calculation of this energy.

• 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 = (4.6 106 kg)(3.00 108 m/s)2

E = 4.1 1011 J

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How much energy is lost or gained when 1 mol of cobalt-60 undergoes beta decay, ? The mass of a atom is 59.933819 amu, and that of a atom is 59.930788 amu.

Sample Exercise 21.9 Calculating Mass Change in a Nuclear Reaction

Practice ExercisePositron emission from 11C, , occurs with release of 2.87 × 1011 J per mole of 11C. What is the mass change per mole of 11C in this nuclear reaction? The masses of 11B and 11C are 11.009305 and 11.011434 amu, respectively.

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A. The atomic mass of iron-56 is the weighted average of the naturally occurring isotopes of iron-56, not just the mass of the nucleus.

B. The values in Table 21.7 reflect only the mass of the nucleus while the atomic mass of iron-56 also includes the mass of its neutrons.

C. The values in Table 21.7 reflect only the mass of the nucleus while the atomic mass of iron-56 also includes the mass of its electrons.

D. The values in Table 21.7 reflect only the mass of the nucleus while the atomic mass iron-56 also includes the mass of its protons.

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A. Yes, nuclei having mass numbers around 100 are not very stable nuclei.

B. No, nuclei have mass numbers around 100 are among the most stable of nuclei.

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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.

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

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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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A. To provide sufficient water to condense the secondary coolant after it passes through a turbine

B. To provide a water pond for storage of nuclear wasteC. To provide steam to heat the reactorD. To provide sufficient coolant to cool the entire operating

environment containing the nuclear reactor

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Country: Most Reactors Most Reactors Highest % Operating Construction

A. China United States GermanyB. United States China FranceC. France China RussiaD. China France Canada

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Nuclear Reactors• The reaction is kept in

check by the use of control rods.

• These rods 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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A. Alpha rays are dangerous only when the alpha emitter is near cells inside the body.

B. Alpha rays do not penetrate the exterior skin effectively but once inside the body they are dangerous to cells.

C. Alpha rays need to be close to blood cells to be damaging but other cells inside the body are far less affected.

D. Alpha rays can penetrate the walls of cells inside the body only when the alpha emitter is in direct contact with the cells.

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A. Absorbed dose, 3 rads; effective dosage, 33 rems.B. Absorbed dose, 5 rads; effective dosage, 50 rems.C. Absorbed dose, 10 rads; effective dosage, 100 rems.D. Absorbed dose, 15 rads; effective dosage, 150 rems.