1. Environmental Physics
Chapter 13: The Building Blocks of Matter
Copyright © 2008 by DBS

2. Introduction

3. Figure 13.1a: Evacuated tube used in observation of cathode rays.
Fig. 13-1a, p. 428

4. Figure 13. 1b: Apparatus used by J. J
Figure 13.1b: Apparatus used by J. J. Thomson (1897) to measure the charge-to-mass ratio of the electron. The evacuated tube is similar to a TV picture tube. The negatively charged particles emitted from the cathode are deflected by either an electric field or a magnetic field. The parallel plates connected to a battery provide the electric field. Two current-carrying coils (not shown) produce a magnetic field perpendicular to the electric field. The sizes of the deflections, as noted on the fluorescent screen, can be used to determine the charge-to-mass ratio of the electron.
Figure 13.1b: Apparatus used by J. J. Thomson (1897) to measure the charge-to-mass ratio of the electron. The evacuated tube is similar to a TV picture tube. The negatively charged particles emitted from the cathode are deflected by either an electric field or a magnetic field. The parallel plates connected to a battery provide the electric field. Two current-carrying coils (not shown) produce a magnetic field perpendicular to the electric field. The sizes of the deflections, as noted on the fluorescent screen, can be used to determine the charge-to-mass ratio of the electron.
Fig. 13-1b, p. 428

5. Figure 13.2: Radioactive elements may emit three types of radiation: electromagnetic radiation called gamma rays; fast-moving electrons called beta particles; and alpha particles, which are the nuclei of helium atoms. If radioactive material is placed at the bottom of a hole in a lead block, radiation will be emitted through the top. If the beam passes through an electric field, it will separate into the three types of radiation.
Figure 13.2: Radioactive elements may emit three types of radiation: electromagnetic radiation called gamma rays; fast-moving electrons called beta particles; and alpha particles, which are the nuclei of helium atoms. If radioactive material is placed at the bottom of a hole in a lead block, radiation will be emitted through the top. If the beam passes through an electric field, it will separate into the three types of radiation.
Fig. 13-2, p. 430

6. Figure 13.3: Scattering of alpha particles from a thin gold foil.
Fig. 13-3, p. 430

7. Figure 13.4: Aerial view of the Fermi National Accelerator Laboratory in Batavia, Illinois, the world’s highest energy particle accelerator. The accelerator ring is 6.3 km (3.8 miles) in circumference. Protons can be accelerated up to 99.99% the speed of light.
Figure 13.4: Aerial view of the Fermi National Accelerator Laboratory in Batavia, Illinois, the world’s highest energy particle accelerator. The accelerator ring is 6.3 km (3.8 miles) in circumference. Protons can be accelerated up to 99.99% the speed of light.
Fig. 13-4, p. 431

8. Figure 13.5: The nucleus of the carbon atom has a positive charge of 6. It is surrounded by six electrons, arranged in two major shells. The number of protons gives the element its atomic number.
Figure 13.5: The nucleus of the carbon atom has a positive charge of 6. It is surrounded by six electrons, arranged in two major shells. The number of protons gives the element its atomic number.
Fig. 13-5, p. 432

9. Figure 13.6: Energy levels of electrons within atoms are analogous to floors in a building. Here, one electron has been excited to a higher state by the addition of heat to the atom.
Figure 13.6: Energy levels of electrons within atoms are analogous to floors in a building. Here, one electron has been excited to a higher state by the addition of heat to the atom.
Fig. 13-6, p. 433

10. Figure 13.7: Spectrum of light emitted by a gas that has been excited by electrical discharge or heat.
Figure 13.7: Spectrum of light emitted by a gas that has been excited by electrical discharge or heat.
Fig. 13-7, p. 434

11. End
Review

12. Nuclear Structure
Atoms are extremely small
10000 x smaller

13. Nuclear Structure Particle Symbol Charge Mass (amu)
Electron e (1/1837)
Proton p
Neutron n
If e- had mass of an orange (100g), a proton would weigh 180 kg (several sacks of potatoes)

14. Nuclear Structure
Isotopes – atoms of the same element with different atomic masses
Same chemical properties
Mass: 1 amu
Most abundant
Mass: 2 amu
‘heavy water’
Mass: 3 amu
Radioactive
Figure 13.8: Isotopes of hydrogen.

15. Nuclear Structure
Mass number (A) should not be confused with atomic mass. Mass number is an integer specific to an isotope and has no units.
Z often omitted since can be obtained from X
Z & N referred to as nucleons

16. Nuclear Structure
e- held in the atom by electrostatic force of attraction
Nucleus held together by strong nuclear force
Short range
>>> electrostatic force
Chemistry – changes in e-
Nuclear physics – changes in p+ and n0 via decay, fission and fusion

17. Nuclear Structure
Atomic no. (Z) defines the element, chemical properties
Isotopes of the same element have the same number of p+, but different numbers of n0 (and therefore different masses)
e.g. carbon-12 and carbon-14
Radioisotope and radionuclide are used to denote unstable, radioatcive isotopes

18. Question
Radon-222 gas is formed from the radioactive decay of radium-226. It enters cracks in basement floors and is the second leading cause of lung cancer
1. Symbolize the isotope in the form AZX
2. Give the number of p+, n0 and e- in an atom of radon-222

19. Radioactivity
Radioactive nuclide is a nuclide that spontaneously undergoes nuclear decay
Results in emission of radiation (particles or rays)
3 types of radiation: alpha, beta and gamma
Figure 13.2: Radioactive elements may emit three types of radiation: electromagnetic radiation called gamma rays; fast-moving electrons called beta particles; and alpha particles, which are the nuclei of helium atoms. If radioactive material is placed at the bottom of a hole in a lead block, radiation will be emitted through the top. If the beam passes through an electric field, it will separate into the three types of radiation.

20. Radioactivity
Ranges of alpha. Beta and gamma rays

21. Radioactivity Particles: alpha (α), beta (β) Waves: gamma (γ)
Particles: alpha (α), beta (β)
Waves: gamma (γ)

22. Radioactivity Alpha decay: 22688Ra → 42He + 22286Rn (α = 42He)
Beta decay: 146C → 147N + 0-1e (β = 0-1e)
Positron emission: 116C → 115B + 01e (anti-electron)
Electron capture: 116C + 0-1e → 115B
gamma-ray (high energy photons) emission
Spontaneous emission of particles from unstable nuclei

23. Radioactive Decay Alpha decay: 22688Ra → 42He + 22286Rn (α = 42He)

24. Radioactive Decay Beta decay: 13755Cs → 13756Ba + 0-1e Neutron splits:
10n → 1+1p + 0-1e
Positron emission:
2211Na → 2210Ne + 01e
Proton splits:
1+1p → 10n + 0+1e

25. Radioactive Decay Gamma decay: 137m56Ra → 13756Ba + γ

26. Question Predict the decay products of the alpha emission of 23994Pu
By law of conservation of mass and energy:
23994Pu → 23592U + 42He

27. Radioactivity Transmutation of elements
Figure 13.9: Example of radioactive decay: the beginning of decay of 238U.

28. Radioactivity
Figure 13.10: The half-life of a nucleus is the time it takes for one half of the original amount of that substance to decay. Radioactive decay is an exponential process.

29. Radioactivity
Half-life: the time required for half the radionuclide to decay
e.g. caesium-137
t1/2 = 30.3 yr

30. Radioactivity Rate of decay is proportional to amount remaining
dN N , let λ = constant  dN = -λN
dt dt
Solve for N,
N = Noe-λt
Where N = no. nuclei at time t, N0 = no. nuclei at start, λ = decay constant
Half-life t1/2 when N = N0 2

31. Question N = Noe-λt Solve for t1/2, N = N0 /2 N0 / 2 = Noe-λt
ln(1/2) = ln(2-1) = -ln2 = - λ t1/2
λ = ln 2
t1/2
Rule of logs
ln ab = b lna

32. Question Derive the expression for the time to decay:
t = t1/2 ln (N / N0) from N = Noe-λt
-0.693

33. Radioactivity Isotope Half-life Nitrogen-16 7 sec Argon-41 1.8 hours
Radon-222
3.8 days
Iodine-131
8 days
Strontium-90
29 years
Radoium-226
1,599 years
Plutonium-239
24,000 years
Uranium-235
7 x 108 years
4.5 x 109 years
Most unstable
Least unstable

34. Radioactivity Radionuclide λ (s-1) t1/2 Lead-210 9.86 x 10-10 22.3 yr
t1/2 is related to probability of any one nuclei decaying
Larger the λ, the higher the probability of decay, the shorter the half-life
With a mix of radioactive waste there is a progression from highly active, short half-life isotopes to less active, long-lived isotopes
Radionuclide
λ (s-1)
t1/2
Lead-210
9.86 x 10-10
22.3 yr
Radon-222
2.11 x 10-6
3.8 d
More active,
More disintergrations

35. 1 Bq = 1 disintergration per second
Radioactivity
Number of atoms that disintergrate per second is called the activity
Measured in Becquerels (Bq):
1 Bq = 1 disintergration per second
Quantity of radioactive substance in which 37 x 109 atoms decay per second has activity of 1 curie (= 1 g Radium)
A = λ N
Where A = activity (Bq), λ = decay constant (= ln2 / t1/2), N = no. radiaoctive atoms present
Short half-lives yield high activities

36. Radioactivity 14C produced via cosmic rays 10n + 147N → 146C + 11H
Atmospheric 14C is found in 14CO2
Incorporated into plants where it decays
Whilst alive 14C/12C ratio is constant
After death 14C no longer replaced from envionment
Useful for about 7 half-lives
Sample must be organic!
t1/2 = 5,730 yr

37. Question
A fossil is found to have 35 % of the amount of carbon-14 of a currently living organism. How old is it?
t = t1/2 ln (N / N0)
-0.693
t = 5730 x ln (35/100)
t = 8680 yrs

38. Turin Shroud

39. Radioactivity
For older objects, rocks and minerals other elements are used
Uses proportions of parent and daughter material
e.g. 238U decays to 206Pb
Measuring % lead in these rocks allows age determination
4.5 billion year t1/2 of 238U allows very old rocks to be dated
e.g. Earth rocks dated to 3.7 billion years, moon 4.2 billion

40. End
Review

41. Nuclear Physics Atomic Mass and Energy
1 amu = 1/12 mass of C-12 nucleus = 1.66 x kg
Energy = mc2
= 1.66 x x (3 x 108)2 = 1.5 x J
1 Electron-volt is the energy gained by e- accelerated in electric field of 1 volt:
E = qV
(Where q = charge on e- = 1.6 x C,  1 eV = 1.6 x J)
Common unit of energy in nucleus is MeV,
1 eV x 1.5 x J = 931 x 106 eV amu = 931 MeV
1.6 x J amu amu

42. Nuclear Physics Stability
Heavy nuclei stable if N > Z
Plot N vs. Z stable nuclei
Linear up to Z = 20, N > Z = neutron excess
Why are only some nuclei stable?
N dilute p+ - p+ repulsion and provide attractive force to balance electric repulsion of increasing p+
Light nuclei stable if N = Z
strong nuclear force

43. Nuclear Physics Stability
Heavy nuclei stable if N > Z
Elements Z > 83 unstable
p+ - p+ repulsion cannot be compensated for by adding N
Light nuclei stable if N = Z

44. Nuclear Physics Binding Energy and Mass Defects
Mass of a nucleus is always less than the sum of the individual masses of the protons and neutrons which constitute it
The difference is a measure of the nuclear binding energy
Calculated from the Einstein relationship: E = Δmc2
For the alpha particle Δm= u which gives a binding energy of 28.3 MeV.

45. Nuclear Physics Binding Energy and Mass Defects
He nucleus does not spontaneously split - energy must be added
Law conservation of energy:
Energy of the composite object + energy expended to split it up = sum of the energies of the separate parts after the split
Energy of the composite object = sum of the energies of its parts - energy needed to split the object apart
[= binding energy]
matom < mparts

46. Nuclear Physics Binding Energy and Mass Defects
Compare to binding energy of an electron in an atom
The nuclear binding energies are on the order of a million times greater than the electron binding energies of atoms

47. Nuclear Physics Binding Energy and Mass Defects
Energy released
Creates heat in nuclear reactor
Heats up the earth’s core
Makes the sun shine
Used to blow up Hiroshima

48. Nuclear Physics Binding Energy and Mass Defects
High binding energy = most stable – difficult to break up
Nuclear Physics Binding Energy and Mass Defects
Explains abundance of Fe
In this region of nuclear size, electromagnetic repulsive forces are beginning to gain against the strong nuclear force
The existence of a maximum in binding energy in medium-sized nuclei is a consequence of the trade-off in the effects of two opposing forces which have different range characteristics. The attractive nuclear force (strong nuclear force), which binds protons and neutrons equally to each other, has a limited range due to a rapid exponential decrease in this force with distance. However, the repelling electromagnetic force, which acts between protons to force nuclei apart, falls off with distance much more slowly (as the inverse square of distance). For nuclei larger than about four nucleons in diameter, the additional repelling force of additional protons more than offsets any binding energy which results between further added nucleons as a result of additional strong force interactions; such nuclei become less and less tightly bound as their size increases, though most of them are still stable. Finally, nuclei containing more than 209 nucleons (larger than about 6 nucleons in diameter) are all too large to be stable, and are subject to spontaneous decay to smaller nuclei.

49. Figure 13.11: Just as it takes energy to pull two magnets apart, energy is also necessary to pull apart the nucleons that are bound together in the nucleus. The total binding energy is the energy required to disassemble the entire nucleus.
Figure 13.11: Just as it takes energy to pull two magnets apart, energy is also necessary to pull apart the nucleons that are bound together in the nucleus. The total binding energy is the energy required to disassemble the entire nucleus.
Fig , p. 440

50. Figure 13. 12: Rutherford’s apparatus to study nuclear reactions
Figure 13.12: Rutherford’s apparatus to study nuclear reactions. The protons p produced in the transmutation of 14N are detected in the scintillator. The incident alpha particles are produced in the decay of the 210Po.
Figure 13.12: Rutherford’s apparatus to study nuclear reactions. The protons p produced in the transmutation of 14N are detected in the scintillator. The incident alpha particles are produced in the decay of the 210Po.
Fig , p. 442

51. Figure 13. 13: Van de Graaff accelerator
Figure 13.13: Van de Graaff accelerator. Nuclei are accelerated by a high-voltage (9 million volts) terminal located within each of the cylindrical tanks. The accelerated particles travel within an evacuated beam tube (shown emerging from the tank). In the foreground is an electromagnet that deflects the beam of particles into a room to the right, where experiments are conducted.
Figure 13.13: Van de Graaff accelerator. Nuclei are accelerated by a high-voltage (9 million volts) terminal located within each of the cylindrical tanks. The accelerated particles travel within an evacuated beam tube (shown emerging from the tank). In the foreground is an electromagnet that deflects the beam of particles into a room to the right, where experiments are conducted.
Fig , p. 443

52. Two types of detectors for measuring radon concentrations
Two types of detectors for measuring radon concentrations. These devices are exposed to air in your home for a specified time, then sent to a laboratory for analysis.
Two types of detectors for measuring radon concentrations. These devices are exposed to air in your home for a specified time, then sent to a laboratory for analysis.
Part (a), p. 444

53. Figure 13. 14: A modern form of the Periodic Table of the elements
Figure 13.14: A modern form of the Periodic Table of the elements. Elements that behave the same chemically are in columns.
Figure 13.14: A modern form of the Periodic Table of the elements. Elements that behave the same chemically are in columns.
Fig a, p. 449

54. Figure 13. 14: A modern form of the Periodic Table of the elements
Figure 13.14: A modern form of the Periodic Table of the elements. Elements that behave the same chemically are in columns.
Figure 13.14: A modern form of the Periodic Table of the elements. Elements that behave the same chemically are in columns.
Fig b, p. 449

55. End
Review

57. Fission 23592U + 10n → 23692U* → 9036Kr + 14456Ba + 210n
Nuclear fission is the splitting of a large nucleus into smaller nuclei
Energy is released because the sum of the masses of these fragments is less than the original mass
23592U + 10n → 23692U* → 9036Kr Ba + 210n

58. Fission → 9037Rb + 14355Cs + 310n energy
Daughter products mass 75 – 160
23592U + 10n → 23692U* → 9036Kr Ba + 210n
→ 9037Rb Cs + 310n
Produce different # 10n
Natural uranium is a mixture of 238/235 isotopes
235U is a fissile isotope (slow neutrons)
only 0.7% natural uranium

59. Fission 23592U + 10n → 23692U* → 14857La + 8535Br + 310n
Uranium-235 = Lanthanum-148 = 148.0
Neutron = Bromine-85 = 84.9
3 neutrons = 3.027
Total = Total =
Δm = = 0.2

60. Fission E = mc2 Consider this: c2 is equal to 9.0 × 1016 m2 s-2
When mass is in kg, the energy units are kg m2 s-2, which is equivalent to 1 joule
1 amu = 1/12 mass of C-12 nucleus = 1.66 x kg
Energy = mc2
= 1.66 x x (3 x 108)2 = 1.5 x J
The large value of c2 means that it should be possible to obtain a tremendous amount of energy from a small amount of matter - whether in a power plant or in a weapon

61. Question
How much energy is theoretically available in 1 kg uranium-235 (25 x 1023) atoms?
1 amu = 1/12 mass of C-12 nucleus = 1.66 x kg
Energy = mc2
= 1.66 x x (3 x 108)2 = 1.5 x J
E = x 1.5 x10-10 J x 25 x 1023
E = 7.1 x 1013 J
E = 71 x 106 MJ
Compared with 29 MJ in 1 kg coal

62. Summary