1. Nuclear Reactions and Their Applications

2. Nuclear Reactions and Their Applications
Radioactive Decay and Nuclear Stability
The Kinetics of Radioactive Decay
Nuclear Transmutation: Induced Changes in Nuclei
Effects of Nuclear Radiation on Matter
Applications of Radioisotopes
Interconversion of Mass and Energy
Applications of Fission and Fusion

3. Comparison of Chemical and Nuclear Reactions
Chemical Reactions
Nuclear Reactions
One substance is converted into another, but atoms never change identity.
Atoms of one element typically are converted into atoms of another element.
Electrons in orbitals are involved as bonds break and form; nuclear particles do not take part.
Protons, neutrons, and other nuclear particles are involved; electrons in orbitals take part much less often.
Reactions are accompanied by relatively small charges in energy and no measurable changes in mass.
Reactions are accompanied by relatively large charges in energy and measurable changes in mass.
Reaction rates are influenced by temperature, concentration, catalyst, and the compound in which an element occurs.
Reaction rates depend on number of nuclei, but are not affected by temperature, catalysts, or, except on rare occasions, the compound in which an element occurs.

4. Components of the Nucleus
>99.9% mass of the atom lies in the dense, tiny nucleus.
A nuclide is a nucleus with a particular composition. Each isotope of an element has a different nuclide.
A particular nuclide is often designated by its mass number; for example, Cl-35 and Cl-37.

5. X Notation for Nuclides
The relative mass and charge of a particle is described by the notation: X A Z
A = mass number
Z = charge of the particle
electron e -1
proton
neutron n 1 p
Example:

6. Nuclear Decay causes Radioactivity
Many nuclides are unstable and spontaneously emit radiation, a process termed radioactive decay.
- The intensity of the radiation is not affected by temperature, pressure, or other physical and chemical conditions.
Nucear decay produces radiation and formation of new element(s).
Three types of natural radioactive emission:
Alpha particles (α, , or ) are identical to helium-4 nuclei. α 4 2
He2+
Beta particles (β, β-, or ) are high-speed electrons. e -1
Gamma rays (γ or ) are very high-energy photons (hv). γ

7. Radioactive emissions in an electric field
The positively charged α particles curve toward the negative plate, the negatively charged β particles curve towards the positive plate, and the γ rays are not affected by the electric field.

8. Nuclear Reaction and Nuclear Equation
When a nuclide decays, it forms a daughter nuclide of lower energy.
The excess energy is carried off by the emitted radiation and the recoiling nucleus of the daughter nuclide.
The decay process is represented by a balanced nuclear equation.
Both the total charge (#Z) and the total mass (#A) must be balanced:
Reactants = Products
Total A
Total Z

9. Modes of Radioactive Decay
Alpha (α) decay: Heavy nuclide decomposes into α particle and a lighter nuclide.
The product nuclide’s A decreases by 4 and Z decreases by 2.
Most common form of decay for a heavy, unstable nucleus.
β- decay produces β- particle and a new nuclide.
A remains the same in the daughter nuclide but Z increases by 1 unit.
228 88
Ra → 63 28
Ni →

10. Positron (β+) emission produces β+ particle and a new nuclide.
The positron is the antiparticle of the electron.
A remains the same in the daughter nuclide but Z increases by 1 unit.
Electron capture: Parent nuclide combines an electron to form a new nuclide.
The effect on A and Z is the same as for positron emission.
Electron capture by Co-57: 11 6
C →

11. Gamma (γ) emission involves the radiation of high-energy γ photons.
Gamma emission usually occurs together with other forms of radioactive decay.
Several γ photons of different energies can be emitted from an excited nucleus as it returns to the ground state.
γ emission results in no change in either A or Z since γ rays have no mass or charge.

12. Modes of Radioactive Decay*

13. Modes of Radioactive Decay*

14. Practice
Writing Equations for Nuclear Reactions
Write balanced equations for the following nuclear reactions:
(a) Thorium-232 undergoes α decay.
(b) Zirconium-86 undergoes electron capture.
(c) Potassium-40 undergoes beta emission
(d) Magnesium-23 undergoes positron emission.

15. Nuclear Stability
Two key factors determine the stability of a nuclide:
- the number of neutrons (N), the number of protons (Z), and their ratio (N/Z), and
- the total mass of the nuclide.
A plot of number of neutrons vs. number of protons for all stable nuclides produces a band of stability that gradually curves above the line for N = Z.
- Lighter nuclides are stable when N = Z.
- As Z increases, the N/Z for stable nuclei gradually increases.
- All nuclides with Z > 83 are unstable.

16. #Neutrons vs. #Protons for the stable nuclides

17. Stability and Nuclear Structure
Protons within the nucleus experience electrostatic repulsive forces, which destabilize the nucleus.
The strong force, which exists between all nucleons, counteracts the weaker repulsive forces.
Nucleons are found in nucleon energy levels, and pairing of the spins of like nucleons leads to greater stability.
- Elements with an even Z (number of protons) usually have a larger number of stable nuclides.
- Over half the stable nuclides have both even N and even Z.

18. Stable Nuclides: Even or Odd matters!
Element
Atomic No. (Z)
No. of nuclides Cd 48 8 In 49 2 Sn 50 10 Sb 51 Te 52 I 53 1 Xe 54 9 Z N
No. of nuclides
Even
157
Odd 53 50 4
TOTAL
264
* Even Z shown in boldface.

19. Predicting the Mode of Decay
Nuclide type
Description
Mode of Decay
neutron-rich
high N/Z
β- decay
neutron → proton, lowers N/Z
proton-rich
low N/Z
β+ emission or e- capture
proton → neutron, increases N/Z
heavy nuclides
Z > 83
α decay
reduces both Z and N

20. The 238U decay series.
A parent nuclide may undergo a series of decay steps before a stable daughter nuclide is formed.

21. Detection and Measurement of Radioactivity
An ionization counter detects radioactive emissions as they ionize a gas.
Ionization produces free electrons and gaseous cations
Gaseous cations are attracted to electrodes and produce an electric current.

22. Detection of radioactivity by an ionization counter.

23. Detection and Measurement of Radioactivity
Scintillation counter detects radioactive emissions by their ability to excite atoms and cause them to emit light.
Radioactive particles strike a light-emitting substance, which emits photons.
The photons strike a cathode and produce an electric current.

24. A scinatillation “cocktail” in tubes to be placed in the counter.

25. Units of Radioactivity
The SI unit of radioactivity is the Becquerel (Bq), defined as one disintegration per second (d/s).
The curie (Ci) is a more commonly used unit:
1 Ci = 3.70x1010 d/s

26. Units of Radiation The gray is the SI unit for energy absorption.
1 Gy = 1 J absorbed per kg of body tissue.
The rad is more widely used: 1 rad = 0.01 J/kg or 0.01 Gy.
The rem is the unit of radiation dosage equivalent to a given amount of tissue damage in a human.
no. of rems = no. of rads x RBE
The RBE is the relative biological effectiveness factor. The rem allows us to assess actual tissue damage by taking into account the strength of the radiation, the exposure time, and the type of tissue.

27. Rate of Radioactive Decay
Radioactive nuclei decay at a characteristic rate, regardless of the chemical substance in which they occur. The rate (A) (= the activity) is the change in number of radioactive nuclide per unit of time
Fact: The rate of radioactive decay is proportional to the number of nuclei present (N).
A = kN
k : decay constant.
The larger k, the higher the activity of the substance.

28. How much radioactive nuclei remains/depleted depends on the Rate of Radioactive Decay
Starting from N0 , at time t, the number of remaining nuclei Nt
ln = -kt or Nt = N0e-kt and ln = kt Nt N0
At time t, the radioactivity of remaining substance
At = kNt = kN0e-kt
ln = -kt or At = A0e-kt At A0

29. Half-Life of Radioactive Decay
The half-life (t1/2) of a nuclide is the time taken for half the nuclei in a sample to decay (Nt = ½ N0 )
- The number of nuclei remaining is halved after each half-life.
- The mass of the parent nuclide decreases while the mass of the daughter nuclide increases
- Activity is halved with each succeeding half-life.
When t = t1/2, Nt = ½ N0 , then

30. Half life of C-14: Loss of 14C nuclei over time
ln 2 k

31. Decay Constants (k) and Half-Lives (t1/2) of Beryllium Isotopes
Nuclide k
t1/2 Be
1.30x10-2/day
53.3 days
1.0x1016/s
6.7x10-17 s
Stable
4.3x10-7/yr
1.6x106 yr
5.02x10-2/s
13.8 s 7 4 8 4 9 4 10 4 11 4

32. Example: Sr-90 occurs as nuclear test and, once ingested, poses long term health hazard. A woman drinks some contaminated milk and ingests g of 90Sr, which is taken up by bones and teeth and not eliminated. (a) How much 90Sr (t1/2 = 29 yr) is present in her body after 10 yr?
k = yr-1, Nt = g

33. Example: Sr-90 occurs as nuclear test and, once ingested, poses long term health hazard. A woman drinks some contaminated milk and ingests g of 90Sr, which is taken up by bones and teeth and not eliminated. (b) How long will it take for 99.9% of the 90Sr to decay?
Nt = 5 x 10-5 g, t = 2.9 x 102 yr

34. Example:
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)?
Given:
N0 = 1.2x1012 d/s t1/2 = 29 yr t = 59 yr
Equation: A = kN
Find: At
At = e26.4 = 2.9x1011 d/s
fraction decayed = 0.76

35. Radioisotopic Dating
t = 1 k A0 At ln
Radioisotopes can be used to determine the ages of certain objects.
Radiocarbon dating measures the relative amounts of 14C and 12C in materials of biological origin.
14C is formed from bombardment of 14N by neutrons
The ratio of 14C/12C remains the same for all living organisms.
Once the organism dies, the amount of 14C starts to decrease (forming 14N).
Since 14C decays at a predictable rate, measuring 14C/12C ratio indicates the time that has passed since the organism died.
40K/40Ar ratios used to determine the age of certain rocks.

36. Ages of several objects determined by radiocarbon dating1 k A0 At ln

37. Radiocarbon Dating PROBLEM:
A sample of an ancient bone has a specific activity of 5.22 disintegrations per minute per gram of carbon (d/min·g). If 12C/14C ratio for living organisms results in a specific activity of 15.3 d/min·g, how old are the bones (t1/2 of 14C = 5730 yr)?
A0 = 15.3 d/min g, At = 5.22 d/min g
k = 1.21x10-4 yr-1
t = 8.89x103 yr

38. Nuclear Transmutation: Element X to Element Y
Nuclear transmutation is the induced conversion of the nucleus of one element into the nucleus of another.
How? High-energy bombardment of nuclei in a particle accelerator.
N + α → p + O

39. Formation of some Transuranium Nuclides*
Reaction
Half-life of Product
239 94
Pu n → Am β 1 -1
241 95
432 yr
Pu α → Cm n 4 2
242 96
Am α → Bk n
243 97
Cm α → Cf n
245 98
253 99
Es α → Md n
256
101
Am O → Lr n 18 8
163 days
4.5 h
45 min
28 s
76 min
* Like chemical reactions, nuclear reactions may occur in several steps.

40. Schematic diagram of a linear accelerator
The linear accelerator uses a series of tubes with alternating voltage. A particle is accelerated from one tube to the next by repulsion.

41. Schematic diagram of a cyclotron accelerator.

42. Effects of Nuclear Radiation on Matter
Radioactive emissions collide with surrounding matter, knocking out electrons and causing ionization
Each such event produces a cation and a free electron.
The number of cation-electron pairs is directly related to the energy of the incoming ionizing radiation.
Ionizing radiation has a destructive effect on living tissue. The danger of a particular radionuclide depends on
- the type of radiation,
- its half-life, and
- its biological behavior.

43. Penetrating power of radioactive emissions
The effect of radiation on living tissue depends on both the penetrating power and the ionizing ability of the radiation.
Penetrating power is inversely related to the mass, charge, and energy of the emission.

44. Molecular Interactions with Radiation
The interaction of ionizing radiation with molecules causes the loss of an electron from a bond or a lone pair.
This results in the formation of free radicals, molecular or atomic species with one or more unpaired electrons.
Free radicals are unstable and extremely reactive.
Reaction between free radicals and live tissues will damage the tissue

45. Sources of Ionizing Radiation
Natural sources of background radiation:
Cosmic radiation from the Sun and stars
Radon is a radioactive product of uranium and thorium decay.
Rn contributes to 15% of annual lung cancer deaths.
Radioactive 40K is present in water and various food sources.
Radioactive 14C occurs in atmospheric CO2.

46. US radon distribution

47. Typical Radiation Doses from Natural and Artificial Sources
Source of Radiation
Average Adult Exposure
Natural
Cosmic radiation
30-50 mrem/yr
Radiation from the ground
From clay soil and rocks
In wooden houses
In brick houses
In concrete (cinder block) houses
~ mrem/yr
10-20 mrem/yr
60-70 mrem/yr
mrem/yr
Radiation from the air (mainly radon)
Outdoors, average value
20 mrem/yr
70 mrem/yr
130 mrem/yr
260 mrem/yr
Internal radiation from minerals in tap water and daily intake of food.
(40K, 14C, Ra)
~ 40 mrem/yr

48. Typical Radiation Doses from Natural and Artificial Sources
Source of Radiation
Average Adult Exposure
Artificial
Diagnostic x-ray methods
Lung (local)
Kidney (local)
Dental (does to the skin)
rad/film
1.5-3 rad/film
≤ 1 rad/film
Locally ≤ 10,000 rad
Therapeutic radiation treatment
Other Sources
Jet flight (4 h)
Nuclear testing
Nuclear power industry
~1 mrem
< 4 mrem/yr
< 1 mrem/yr
Total average value
mrem/yr

49. Acute Effects of a Single Dose on Whole-Body Irradiation

50. Radioactive Tracers
The isotopes of an element exhibit very similar chemical and physical behavior.
A small amount of radioactive isotope mixed with the stable isotope will undergo the same chemical reactions, and can act as a tracer.
Radioactive tracers are used
to study reaction pathways,
to track physiological functions,
to trace material flow,
to identify the components of a substance from a very small sample, and
to diagnose a wide variety of medical conditions.

51. PET and brain activity
These PET scans show brain activity in a normal person (left) and in a patient with Alzheimer’s disease (right). Red and yellow indicate relatively high activity within a region.

52. Some Radioisotopes Used as Medical Tracers Isotope
Body Part or Process
11C, 18F, 13N, 15O
PET studies of brain, heart
60Co, 192Ir
Cancer therapy
64Cu
Metabolism of copper
59Fe
Blood flow, spleen
67Ga
Tumor imaging
123I, 131I
Thyroid
111In
Brain, colon
42K
Blood flow
81mKr
Lung
99mTc
Heart, thyroid, liver, lung, bone
201Tl
Heart muscle
90Y
Cancer, arthritis

53. Other Applications of Ionizing Radiation
Radiation therapy
Cancer cells divide more rapidly than normal cells, and are therefore susceptible to radioisotopes that interfere with cell division.
Destruction of microbes
Irradiation of food increases its shelf life by killing microorganisms that cause rotting or spoilage.
Insect control
Power for spacecraft instruments

54. FDA: The increased shelf life of irradiated food

55. The Interconversion of Mass and Energy
The total quantity of mass-energy in the universe is constant.
Any reaction that releases or absorbs energy also loses or gains mass.
E = mc2 or ΔE = Δmc2 so Δm = ΔE c2
In a chemical reaction, the energy changes in breaking or forming bonds is relatively small, so mass changes are negligible.
In a nuclear reaction, the energy changes are enormous and the mass changes are easily measurable.

56. Nuclear Binding Energy: E = mc2
The mass of the nucleus is less than the combined masses of its nucleons. C-12 atom exactly amu, free nucleons together weighs amu
- Mass always decreases when nucleons form a nucleus, and the “lost” mass is released as energy.
- Energy is required to break a nucleus into individual nucleons.
1 amu = x 106 eV = MeV
The nuclear binding energy is the energy required to break 1 mol of nuclei into individual nucleons.
Binding energy = (Mass (proton + neutron) – Mass atom) x MeV/1 amu

57. 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 = amu; mass of 1H atom = amu; mass of neutron = amu).
8.790 MeV/nucleon

58. Binding Energy/Nucleon vs. Mass Number
The greater the binding energy per nucleon, the more stable the nuclide.

59. Fission or Fusion
The binding energy per nucleon peaks at elements with mass number A ≈ 60.
- Nuclides become more stable with increasing number up to around 60 nucleons, after which stability decreases.
There are two ways nuclides can increase their binding energy per nucleon:
A heavier nucleus can split into lighter ones by undergoing fission.
Lighter nuclei can combine to form a heavier nucleus in a process called fusion.

60. Fission of 235U caused by neutron bombardment.

61. Nuclear Fission
The splitting of large nuclei into smaller nuclei, initiated by neutron bombardment, releasing more high energy neutrons and more energy
Fission releases energy and generates more high-energy neutrons, which cause further fission to occur.
The fission process becomes self-sustaining by a chain reaction. The mass required to achieve this is called the critical mass.
The energy from nuclear fission can be harnessed and converted to other forms of energy.

62. A chain reaction involving fission of 235U.

63. An atomic bomb based on 235U.
An atomic bomb uses an uncontrolled chain reaction to produce a powerful explosion.

64. A light-water nuclear reactor.

65. The tokamak design for magnetic containment of a fusion plasma.

66. Chemical Connections
Element synthesis I the life cycle of a star.

67. Predicting the Mode of Nuclear Decay
Sample Problem
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) B (b) U (c) As (d) La

68. SOLUTION:
(a) 12B has Z = 5 and its atomic mass is The nuclide’s A value of 12 is significantly higher than its atomic mass, so it is neutron rich.
It will probably undergo β- decay.
(b) 234U has Z = 92, so it will undergo α decay and decrease its total mass.
(c) 81As has Z = 33 and its atomic mass is The A value of 81 is much higher than the atomic mass, so it is neutron rich and will probably undergo β- decay.
(d) 127La has Z = 57 and its atomic mass is The A value of 127 is much lower than the atomic mass, so it is proton rich and will probably undergo β+ emission or e- capture.