Environmental Physics

Chapter 13:The Building Blocks of Matter

Copyright © 2008 by DBS

Introduction

Fig. 13-1a, p. 428

Figure 13.1a: Evacuated tube used in observation of cathode rays.

Fig. 13-1b, p. 428

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. 13-2, p. 430

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. 13-3, p. 430

Figure 13.3: Scattering of alpha particles from a thin gold foil.

Fig. 13-4, p. 431

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. 13-5, p. 432

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. 13-6, p. 433

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. 13-7, p. 434

Figure 13.7: Spectrum of light emitted by a gas that has been excited by electrical discharge or heat.

End

• Review

Nuclear Structure

• Atoms are extremely small

10000 x smaller

Nuclear Structure

Particle Symbol Charge Mass (amu)

Electron e- -1 0.000544 (1/1837)

Proton p+ +1 1.007277

Neutron n0 0 1.008665

If e- had mass of an orange (100g), a proton would weigh 180 kg (several sacks of potatoes)

Nuclear Structure

• Isotopes – atoms of the same element with different atomic masses

• Same chemical properties

Figure 13.8: Isotopes of hydrogen.

Mass: 3 amuRadioactive

Mass: 1 amuMost abundant

Mass: 2 amu‘heavy water’

Nuclear Structure

Z often omitted since can be obtained from X

Z & N referred to as nucleons

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

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

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

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.

Radioactivity

• Ranges of alpha. Beta and gamma rays

Radioactivity

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

Radioactivity

• Alpha decay: 22688Ra → 4

2He + 22286Rn (α = 4

2He)

• Beta decay: 146C → 14

7N + 0-1e (β = 0

-1e)

• Positron emission: 116C → 11

5B + 01e (anti-electron)

• Electron capture: 116C + 0

-1e → 115B

• gamma-ray (high energy photons) emission

Spontaneous emission of particles from unstable nuclei

Radioactive Decay

Alpha decay:

22688Ra → 4

2He + 22286Rn

(α = 42He)

Radioactive DecayBeta decay:

13755Cs → 137

56Ba + 0-1e

Neutron splits:10n → 1

+1p + 0-1e

Positron emission:

2211Na → 22

10Ne + 01e

Proton splits:1+1p → 1

0n + 0+1e

Radioactive Decay

Gamma decay:

137m56Ra → 137

56Ba + γ

Question

Predict the decay products of the alpha emission of 23994Pu

By law of conservation of mass and energy:

23994Pu → 235

92U + 42He

Radioactivity

• Transmutation of elements

Figure 13.9: Example of radioactive decay: the beginning of decay of 238U.

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.

Radioactivity

Half-life: the time required for half the radionuclide to decay

e.g. caesium-137t1/2 = 30.3 yr

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

Question

N = Noe-λt

Solve for t1/2, N = N0 /2

N0 / 2 = Noe-λt

1/2 = e-λt

ln(1/2) = ln(2-1) = -ln2 = - λ t1/2

λ = ln 2

t1/2

Rule of logs

ln ab = b lna

Question

Derive the expression for the time to decay:

t = t1/2 ln (N / N0) from N = Noe-λt

-0.693

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

Uranium-235 4.5 x 109 years

Most unstable

Least unstable

Radioactivity

• 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

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

Radioactivity

• 14C produced via cosmic rays

10n + 14

7N → 146C + 1

1H

• 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

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) -0.693t = 5730 x ln (35/100)

-0.693

t = 8680 yrs

Turin Shroud

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

End

• Review

Nuclear Physics Atomic Mass and Energy

• 1 amu = 1/12 mass of C-12 nucleus = 1.66 x 10-27 kgEnergy = mc2

= 1.66 x 10-27 x (3 x 108)2 = 1.5 x 10-10 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 10-19 C, 1 eV = 1.6 x 10-19 J)

• Common unit of energy in nucleus is MeV,

1 eV x 1.5 x 10-10 J = 931 x 106 eV 1 amu = 931 MeV1.6 x 10-19 J 1 amu amu

Nuclear Physics Stability

• Plot N vs. Z stable nuclei• Linear up to Z = 20,

N > Z = neutron excess

Why are only some nuclei stable?

strong nuclear forceLight nuclei stable if N = Z

Heavy nuclei stable if N > Z

N dilute p+ - p+ repulsion and provide attractive force to balance electric repulsion of increasing p+

Nuclear Physics Stability

• Elements Z > 83 unstable

• p+ - p+ repulsion cannot be compensated for by adding N

Light nuclei stable if N = Z

Heavy nuclei stable if N > Z

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= 0.0304 u which gives a binding energy of 28.3 MeV.

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

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

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

Nuclear Physics Binding Energy and Mass Defects

Explains abundance of FeHigh binding energy = most stable – difficult to break up

In this region of nuclear size, electromagnetic repulsive forces are beginning to gain against the strong nuclear force

Fig. 13-11, p. 440

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. 13-12, p. 442

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. 13-13, p. 443

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.

Part (a), p. 444

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.

Fig. 13-14a, p. 449

Figure 13.14: A modern form of the Periodic Table of the elements. Elements that behave the same chemically are in columns.

Fig. 13-14b, p. 449

Figure 13.14: A modern form of the Periodic Table of the elements. Elements that behave the same chemically are in columns.

End

• Review

Fission

• 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 + 1

0n → 23692U* → 90

36Kr + 14456Ba + 21

0n

Fission

• Daughter products mass 75 – 160

23592U + 1

0n → 23692U* → 90

36Kr + 14456Ba + 21

0n

→ 9037Rb + 143

55Cs + 310n

• Natural uranium is a mixture of 238/235 isotopes

235U is a fissile isotope (slow neutrons)

only 0.7% natural uranium

Produce different # 1

0n

energy

Fission

Uranium-235 = 235.1 Lanthanum-148 = 148.0

Neutron = 1.009 Bromine-85 = 84.9

3 neutrons = 3.027

Total = 236.109 Total = 235.927

Δm = 0.182 = 0.2

23592U + 1

0n → 23692U* → 148

57La + 8535Br + 31

0n

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 10-27 kg

Energy = mc2

= 1.66 x 10-27 x (3 x 108)2 = 1.5 x 10-10 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

Question

How much energy is theoretically available in 1 kg uranium-235 (25 x 1023) atoms?

E = 0.182 x 1.5 x10-10 J x 25 x 1023

E = 7.1 x 1013 JE = 71 x 106 MJ

Compared with 29 MJ in 1 kg coal

1 amu = 1/12 mass of C-12 nucleus = 1.66 x 10-27 kg

Energy = mc2

= 1.66 x 10-27 x (3 x 108)2 = 1.5 x 10-10 J

Summary