Chapter 24

Nuclear Reactions and Their Applications

The behavior of three types of radioactive emissions in

an electric field

Types of Radioactive Decay: Balancing Nuclear Equations

Total ATotal Z Reactants = Total A

Total Z Products

Alpha decay - A decreases by 4 and Z decreases by 2. Every element heavier than Pb undergoes decay.

Beta decay - ejection of a particle from the nucleus from the conversion of a neutron into a proton and the expulsion of 0

-1. The product nuclide will have the same Z but will be one atomic number higher.

Positron decay - a positron (01) is the antiparticle of an electron. A

proton in the nucleus is converted into a neutron with the expulsion of the positron. Z remains the same but the atomic number decreases.

Electron capture - a nuclear proton is converted into a neutron by the capture of an electron. Z remains the same but the atomic number decreases.

Gamma emission - energy release; no change in Z or A.

Sample Problem 1 Writing Equations for Nuclear Reactions

PROBLEM: Write balanced equations for the following nuclear reactions:

(a) Naturally occurring thorium-232 undergoes decay.

(b) Chlorine-36 undergoes electron capture.

Nuclear Stability and Mode of Decay

•Very few stable nuclides exist with N/Z < 1.

•The N/Z ratio of stable nuclides gradually increases a Z increases.

•All nuclides with Z > 83 are unstable.

•Elements with an even Z usually have a larger number of stable nuclides than elements with an odd Z.

•Well over half the stable nuclides have both even N and even Z.

Predicting the Mode of Decay

•Neutron-rich nuclides undergo decay.

•Neutron-poor nuclides undergo positron decay or electron capture.

•Heavy nuclides undergo decay.

A plot of neutrons vs. protons for the stable nuclides

Sample Problem 2 Predicting Nuclear Stability

PROBLEM: Which of the following nuclides would you predict to be stable and which radioactive? Explain.

(a) 1810Ne (b) 32

16S (c) 23690Th (d) 123

56Ba

Sample Problem 3 Predicting the Mode of Nuclear Decay

PROBLEM: Predict the nature of the nuclear change(s) each of the following radioactive nuclides is likely to undergo:

(a) 125B (b) 234

92U (c) 7433As (d) 127

57La

The 238U decay series

Decay rate (A) = N/t

SI unit of decay is the becquerel (Bq) = 1d/s.

curie (Ci) =

number of nuclei disinegrating each second in 1g of radium-226 =

3.70x1010d/s

Nuclear decay is a first-order rate process.

Large k means a short half-life and vice versa.

Decrease in the number of 14C nuclei over time

Sample Problem 4 Finding the Number of Radioactive Nuclei

PROBLEM: Strontium-90 is a radioactive by-product of nuclear reactors that behaves biologically like calcium, the element above it in Group 2A(2). When 90Sr is ingested by mammals, it is found in their milk and eventually in the bones of those drinking the milk. If a sample of 90Sr has an activity of 1.2x1012 d/s, what are the activity and the fraction of nuclei that have decayed after 59 yr (t1/2 of 90Sr = 29 yr)

Radiocarbon dating for determining the age of artifacts

Sample Problem 5 Applying Radiocarbon Dating

PROBLEM: The charred bones of a sloth in a cave in Chile represent the earliest evidence of human presence in the southern tip of South America. A sample of the bone has a specific activity of 5.22 disintegrations per minute per gram of carbon (d/min*g). If the ratio of 12C:14C in living organisms results in a specific activity of 15.3 d/min*g, how old are the bones? (t1/2 of 14C = 5730 yr)

A linear accelerator

The linear accelerator operated by Stanford University, California

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

The cyclotron accelerator

Penetrating power of radioactive emissions

Penetrating power is inversely related to the mass and charge of the emission.

Nuclear changes cause chemical changes in surrounding matter by excitation and ionization.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

The use of radio-isotopes to image the

thyroid gland

asymmetric scan indicates disease

normal

PET and brain activity

normal Alzheimer’s

The increased shelf life of irradiated food

The Interconversion of Mass and Energy

E = mc2

E = mc2

m = E / c2

The mass of the nucleus is less than the combined masses of its nucleons. The mass decrease that occurs when nucleons are united into a nucleus is called the mass defect.

The mass defect (m) can be used to calculate the nuclear binding energy in MeV.

1 amu = 931.5x106 eV = 931.5MeV

Sample Problem 6 Calculating the Binding Energy per Nucleon

PROBLEM: Iron-56 is an extremely stable nuclide. Compute the binding energy per nucleon for 56Fe and compare it with that for 12C (mass of 56Fe atom = 55.934939 amu; mass of 1H atom = 1.007825 amu; mass of neutron = 1.008665 amu).

The variation in binding energy per nucleon

Induced fission of 235U

A chain reaction of 235U

Diagram of an atomic bomb

The tokamak design for magnetic containment

of a fusion plasma

Detection of radioactivity by an ionization counter

Vials of a scintillation “cocktail” emitting light

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A view of Supernova 1987A