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Ionizing Radiation– radioactivity measurements

In general, radiation refers to travel of photons in space, but the term is also used to mean subatomic particles emitted by radioactive nuclides or generated by machines. These particles and photons usually ionize the molecules or atoms along their tracks, and they are called ionizing radiation. Radiation such as infrared, microwave, long radio wave, and visible light that do not ionize atoms or molecules on its path are called non-ionizing radiation.

Ionizing radiation includes , , protons, X-rays, cosmic rays, and gamma rays. In this Chapter, we shall discuss their interactions with materials. Their interactions allow us to built detectors and counters for their measurements. Details of interaction at the atomic or sub-atomic level are particularly interesting.

Strictly speaking, neutrons do not cause ionization. However, they induce radioactivity, and eventually lead to ionization. Nevertheless, they deserve particular attention.

Heisenberg pointed out that observations disturb the system being observed, during the pronouncement of his uncertainty principle. Properties not being observed are affected during a measurement. Actually, interactions link the observer to the observed.

Ionizing radiation is everywhere. We encounter it in our daily lives. Ionizing radiation has been blamed for aging, illness, environmental damage, skin cancer, and the destruction of immune responses. No doubt, ionizing radiation causes special chemical phenomena, one of which is the generation of radicals. Initiatiating polymerization reactions are one of the important industrial applications.

Radiation effects in biology are studied due to health and safety concerns. From a medical point of view, radiation may induce certain type of disease such as cancer. On the other hand, they may have special effect on diseased cells. Radiation induces chromosome and DNA sequence changes that affect future generations.

The perturbation of a system to be observed caused by the observation is also an important factor in determining the limits within which a visual description of atomic phenomena is possible.

Werner Heisenberg─an opening statement of the uncertainty principle

High-Energy RadiationIonizing radiation consists of high-energy particles and high-energy photons. High-energy radiation may be emitted by atoms (X-rays), nuclei (protons, , , and rays), or accelerators (atomic nuclei and others).

High-energy particles are moving at very high speed. When passing by atoms or molecules, they knock out one or more electrons from them, producing positive ions and electrons. A positive ion and an electron make an ion pair, for example, O+ and e– or O+

2 and e–.

In addition to ionization, there are other mechanisms by which energetic particles loose energy. For the consideration of interactions between ionizing radiation and material, the particles are divided in the following categories.

heavy charged particles such as protons, particles, energetic nuclei, mesons, and hadrons.

light charged particles such as electrons, positrons and other leptons. electromagnetic radiation in the forms of X-rays and rays, and neutral particles such as neutrons.

Discovery of Ionization by RadiationX-rays and radioactivity discharged a charged electroscope, observed Curie, Rutherford and others when they worked with radioactivity.

What causes the discharge of electroscope?How does X-rays and radioactivity discharge a charged electroscope? Can electroscopes be used as ionizing radiation detectors?

An electroscope consists of two gold leaves suspended from a metallic conductor in a glass jar. Glass and air are insulators. Touching the conductor with electric charges makes the leaves stay apart in a charged state because like charges repel each other. Conducting the charges away or neutralizing them with opposite charges causes the leaves to collapse into a discharged state.

When a charge electroscope is exposed to X-rays or radioactivity, the electroscope becomes discharged. Early researchers such as Curie and Rutherford interpreted the discharge as due to the ionization of radiation. Ion pairs produced by radiation make air a conductor. Opposite charges attract to the leaves neutralized the charge.

Energies associated with molecules can be divided into kinetic energies of translation, vibration and rotation and energies associated with electronic energy states. Small amounts of energies excite molecules by changing their electronic states, or kinetic energies of rotation, vibration, and translation (temperature change). Large amounts of energies break up chemical bonds and electrons. When one or more electrons break away, molecules or atoms are ionized. The ions so formed carry a single or multiple units (charge of electron) of positive charges.

The minimum energy required to remove an outer electron from atoms or molecules is called ionization energy. Ionization energies of some common substances and the ionization processes are shown in a box here. The equations in the box indicate the amounts of energy required for the ionization process. For example, 14 eV will strip an electron off the oxygen diatomic molecule. Electrons stripped off an atom or molecule with minimum energy have no kinetic energy. If more energy is transferred to the electron, it will leave an atom or a molecule with a kinetic energy. Ionizing radiation removes electrons and usually leaves them with some kinetic energy. Recombination of electron with its ion does not occur, unless the kinetic energy of the electron is dissipated. Collisions cause the kinetic energy of electrons to be dissipated to other molecules. Low-energy electrons are picked up by atoms and ions.

More energy is required to remove an inner-shell electron or from an ion. Ionization by radiation removes electrons of inner and outer shells, and sometimes bonding electrons. The average energy required to generate an ion pair by radiation is higher than the first ionization energy. For example, some average energies for ion pair production in some familiar media are listed:

Average Ionization Energy (IE eV) per Pair of Some Common Substances

Material Air Xe He NH3 Ge-crystalAverage IE 35 22 43 39 2.9

In the table above, all substances are gases except for Ge crystals. Thus, for the same ionizing radiation, the number of ion pairs generated depends on the material. Note that very low energy is required to produce an ion pair in a Ge crystal, which is a semiconductor. Germanium (Ge) and other semiconductor crystals are very sensitive ionizing radiation detectors because they give large signals due to the low ionization energy.

Ionization Energy and Ionization

O2 + 14 eV O2+ + e-

H2 + 15 eV H2+ + e-

He + 25 eV He+ + e-

He+ + 54 eV He2+ + e-

H2O + 13 eV H2O+ + e-

CO2 + 14 eV CO2+ + e-

N2 +16 eV N2+ + e-

The production of ion pairs by a high-energy particle on its path is depicted in a diagram here. Electrons removed from atoms and molecules by radiation are called primary electrons. Some of these electrons carry a very high kinetic energy, and they, like the rays, cause further ionization. Electrons knocked out by primary electrons are secondary electrons.

Ionizing radiation interacts with many atoms per unit length on its path. A gas at 273 K and 1.0 atm has 2.71022 molecules per liter, or 2.71019 molecules per ml (=cm3). Gas molecules on average travel a short distance (210-7 m or 0.2 micrometer) between collisions. This distance is called mean free path. A liter of water contains 3.3 x 1025 molecules, 1,200 times denser than that of a gas. Atomic densities in solids are similar. Densities affect the movements of electrons, ions, and molecules. Due to the excess energy, however, recombination of ion pairs reaches an equilibrium and the net number of ion pairs remain constant for a period.

Review Questions

1. On the path of an alpha particle, nearly all molecules are ionized. If the average energy required to produce an ion pair is 35 eV, how many pairs of ions are produced by a 1.0-MeV alpha particles? What is the total amount of charge (both positive and negative) produced?

2. At standard temperature and pressure (STP), 1 mole of gas occupies 22.4 L of volume. Calculate the molecular density per cm3 of gas at STP.

Heavy Charged Particles Alpha () particles, protons, atomic nuclei from particle accelerators, and baryons are heavy charged particles. They lose energy in the medium mostly by ionization*.

How fast do high-energy heavy particles move?What are the factors affecting the energy loss of particles in a medium?How far do heavy particles travel in a medium?

* See also properties of mesons and baryons (collectively called hadrons). They decay into other high energy particles.

Ion Pairs on a Radiation Path

│ooooooooooooooooo│ │oooooooooooooooo│ │oooooooo+-ooooooo│ |oooooo-+ooooooooo│

│oooo+-ooooooooooo│ │oo-+ooooooooooooo│ │+-ooooooooooooooo│|ooooooooooooooooo││ooooooooooooooooo│

o Atoms and molecules in a medium.

Alpha () particles and heavy ions interact with electrons via Coulomb force of attraction. However, these particles are moving at high speed through their media. A classical approach to calculate the velocity shown below gives the approximate speed. For example, if the kinetic energy of an particle is 1 MeV, its velocity can be calculated, by using a mass of 41.6610-27 kg,

1 MeV = 1.60 x 10-13 J = (½) (41.6610-27 kg) v2

v2= 4.821013 (m/s)2

v = 6.9106 m/s

Since this speed is only a fraction of the speed of light (3108 m/s), the result is reasonably correct.

Electrons are pulled away by positive particles despite their high speed of motion. Because the radius of an atom is 100000 times larger than that of a nucleus, the heavy particles only occasionally colliding with a nucleus and they travel in almost straight lines, interacting with mostly electrons. On their path, particles and ions knock electrons out of their atomic or molecular orbitals, often leading to multiple ionization. The ionization process generates free electrons and positive ions or ion pairs on their path. The ionization process can be represented by

A An+ + n e–,

where n is an integer indicating the number of ion pairs. Again, energetic primary electrons cause further ionization in a cascade to produce secondary ion pairs.

There may be cases in which the electrons are not removed from the atoms, but the electrons acquire some energy from the particle. Such a process excites a molecule. Ionization and excitation of the electrons rupture chemical bonds and generate free radicals. Free radicals are reactive species and they cause further chemical reactions.

The Born-Bethe Formula for Energy Loss of Charged Particles.

- dEdx

= KM z

E

2

Energy loss per distance (-dE/dx) is proportional to the mass, M, and square of charge, z2, but inversely proportional to its energy E. The distance of the track is represented by x, and K is a constant.

The stopping power of a medium is the rate of energy loss per unit distance along the path. Born and Bethe have shown that the stopping power of a medium is proportional to the mass M, and to the square of atomic number, Z2, of the atoms in the medium. Thus, a medium consisting of heavy atoms have high stopping power. However, the stopping power is inversely proportional to the energy of the particle. A fast moving particle deposit less energy per unit length on its track. High stopping power results in generating high ion pair density.

The stopping power of the medium is relatively small at the time when an particle enters the medium because its energy is high. As it travels through the medium, it loses energy and the stopping power increases. Thus, the ion pairs density generated along the paths of a particle is low at the time when it enters the medium, and increases to a maximum called Bragg peak just before it stops. A plot of ion density as a function of the distance in the medium is called a Bragg curve. Such a curve has a general shape as shown here.

Heavy particles lose energy in a medium at a faster rate than light particles. Thus, they generate higher ion-pair densities on their tracks. Alpha particles generate denser ion-pair densities than protons of the same kinetic energy in the same type of media.

Heavy particles such as protons and particles of certain energy will lose all their energy in a definite distance in a medium, and this distance is called the range, which depends on charge, mass, and the kinetic energy of the incident particles. One-MeV particles have a shorter range than 5-MeV ones, and protons have longer range than particles if they have the same kinetic energy. The range also depends on the nature of the medium. Five-MeV particles have a range of several centimeters in air, but less than a millimeter in water or a solid material. The range is determined by measuring the intensity with an absorber between the detector and the source. The thickness at which the intensity drops to half is the range. The experiment and graphic determination of range measurement is depicted here.

The stopping power of the medium depends on the atomic weights and densities. A medium consisting of heavy elements such as lead have a larger stopping power than one

Ion Pair Density Along the Path of HeavyCharged Particles in a Medium

Distance along the path

Ion pairsdensity particle

proton

Variation of Intensity as a Function of ThicknessDetector

Absorber

Intensity

thickness

sourcestraggling

Range

consisting of light elements. A gas has low stopping power due to low density. Since the interaction of heavy particles with the atoms in the medium is a matter of chance, there is a scattering of ranges for particles of the same energy. This scattering is referred to as the range straggling.

Ranges in pure aluminum as functions of energies have been carefully measured for alpha particles and protons. The low atomic number (Z = 13) of aluminum makes ranges in it long. Measuring long ranges is easier and more precise. Thus, ranges in aluminum have been the standards and ranges are usually expressed in mass per unit area, (mg cm–2, converted by using lengthdensity). By measuring the range of a particle source, its energy can be determined by comparing with a known standard. Decay energies of many emitters have been tabulated, and range measurements can be used to identify sources. Knowing the range, a shield thicker than the range of the particles offers radiation protection, because it will stop all the radiation from passing through.

Heavy charged particles usually have short ranges. The range of alpha particles from radium in air at 298 K and 1 atm is 7.1 cm, and the Bragg peak appears 6.3 cm from the source. There are about 143,000 ion pairs on its track, giving an average 20,000 ion pair per cm along the track. These alpha particles cannot penetrate a sheet of paper, and they may not be able to penetrate the membrane that separates the gas in the detector from the environment. Thus, commercial radioactivity detectors may not be able to detect the alpha particles.

Generally, when the velocities of protons and alpha particles are high, they do not pick up electrons in the medium. They begin to pick up electrons only when their kinetic energies are comparable to those of ions or atoms in the medium. After they pick up required electrons, they become part of the medium. Elastic and inelastic collisions become the dominant interactions thereafter.

Review Questions

1. Estimate the velocities of protons whose kinetic energies are 1.0 and 0.1 MeV respectively using the method of Newtonian physics. Discuss the result.

2. How is the range of particles measured? What purposes do the range measurement serve?

3. How many ion pairs are formed in the path of a 1.0 MeV proton, if the average energy required to produce an ion pair is 35 eV? If the range of the proton is 10 cm, calculate the number of ion pairs per cm on its path. For a 5.0-MeV particle, the range is to 7.2 cm. Evaluate the number of ions and ion pair density per cm on its path.

Light Charged ParticlesParticles with mass comparable to those of electrons are light charged particles. Essentially, they are high-speed positron and electrons. Their rest mass is only 1/1850 amu., much lighter than those of protons. They interact with electrons of the media.

How do light charged particles lose energy in a medium? Why and how they are different from the heavy charged particles?

Let us use the Newtonian physics to estimate of the speed of a particle whose kinetic energy is 1.0 MeV. Assume the velocity to be v, then the kinetic energy is (1/2) m v2. Thus,

1 MeV = 1.610-13 J= (1/2) m v2

= (1/2) (9.110-31 kg v2

Solving for v, v2 = 3.301017

orv = 5.7108 m/sec.

This speed exceeds the speed of light, (3.0108 m/sec), and it violates principle of limiting speed. The theory of relativity must be considered for a proper calculation of the velocity or speed of a high-energy electron. The mass, m, of a 1-MeV beta particle is actually 1.51 MeV, rather than 0.51 MeV. In general, for a particle of kinetic energy Ek, its mass in amu is,

Ek MeV + 0.51 MeV (rest mass of electron)m = ─────────────────────────────── amu

931.5 MeV

The velocity, v, is then calculated by the equation

where c is the velocity of light, and mo is the rest mass of the electron. The velocity is 81% the speed of light, still a very high value.

The interactions of beta particles with matter is similar to those of other charged particles such as protons and alpha particles, but a high speed electron may lose half of its kinetic energy in a single encounter with an electron in the stopping medium. Thus, it may suffer a considerable deflection causing it to travel in a zigzag path. An imaginary path is depicted here to show the scattering of electron. Electrons with energy less than 1.02 MeV lose energy by elastic and inelastic scattering. Scattering causes ionization and excitation of electrons in the medium. Of course, the electron leaving a medium may not be the same electron that enters the medium. Electrons have no individual identity.

The range of monoenergetic electrons (all have the same kinetic energy) is not a well defined quantity compared to those of heavy charged particles. There is more range straggling. In spite of the severe range straggling, kinetic energies of electrons can be estimated approximately by means of extrapolation. The extrapolation and the range straggling as seen from the plot of their intensity (I) after they pass an absorber of thickness x is shown in a sketch here. The measurement of intensity is done in a similar way as that used for heavy charged particles discussed in the previous section. Electrons have a greater range than protons if they all have the same kinetic energy, but the intensity drops gradually as the thickness increases. In contrast, the intensity of heavy particles remains essentially constant as the thickness increases until the thickness is approximately equal to the range.

An Imaginary Path of a particle ina Medium

Intensity (I ) of Electrons with the Same Kinetic Energyas a Function of Thickness (x) of Absorber.

I

x

Extrapolatedrange

Rangestraggling

absorberI0

Idetector

I0

x

Collision between beta particles and electrons causes ionization and excitation of the electrons in the medium. In addition, high-speed electrons passing by atomic nuclei experience attraction and repulsion. They are accelerated or decelerated in a medium. Acceleration and deceleration of charges cause them to emit photons at the expense of their kinetic energy. Photons so emitted are known as bremsstrahlung radiation (braking radiation). Their properties are similar to those of X-rays. Beta particles and positrons of very high energy (100 MeV) lose their energy almost exclusively by bremsstrahlung radiation from their interaction with fields of nuclei in the medium.

Positrons, +, combine with electrons to form short-lived systems called positroniums, which decay with a half life of 0.1 microseconds into two photons each. Such a process is called annihilation, in which both particles disappear and their masses convert to the energy of two photons (gamma rays). Annihilation is the main mode of interaction between the short-lived positron and mater. Recall that positrons from cosmic rays were discovered not from annihilation with electron, but from their ionization track showing them being deflected in the opposite direction from that of electrons. Thus, positrons also produce ion pairs before they were annihilated by electrons.

Bremsstrahlung radiations, annihilation and ionization are the major modes of interactions of high-speed electrons with the medium. A diagram indicating the three interaction modes by which the particles lose energy in a matter is given here.

Review Questions

1. Estimate the velocities of electrons whose kinetic energies are 10.0 and 0.01 MeV respectively. Discuss the results.

2. What are the three major mechanisms by which electrons lose their energies in a medium.

3. Draw a Feynman diagram for the annihilation of positrons and electrons.

Bremsstrahlung Radiation and itsFeynmann Diagram

E = h v

e– .h v

Feynmanndiagram

Ionizationization

Braking radiation

Annihilation

Electromagnetic RadiationThe energies of a photon in the deep-red region and in the blue region of the visible light are 1.5 and 3.0 eV respectively. The UV radiation covers a wide energy range from a few eV to hundreds eV. X-ray photons have energies in the order of keV The boundary between X-rays and -rays is a blur one, and but in general -ray photons have energies in the order of MeVs. Photons have a very wide range of energies and they interact with matter in many different ways. Photons with energies higher than a few keV are ionizing radiation.

What are the properties of high-energy electromagnetic radiation?How do they lose energy in a medium?What are the processes by which X-rays and -ray loose energy?

The X-ray and -ray photons lose their energy in a stopping medium mainly by these major processes: photoelectric effect, Compton effect, and pair production. Photoelectric and Compton effects produce ion pairs, and pair production produces a pair of electron and positron from a photon.

When all the energy (E = h ) of a X-ray and -ray photon is used to release the electron from an atom or molecule, the process is called photoelectric effect. From the principle of conservation of energy, the kinetic energy of the electron so released is equal to the energy of the photon (h ) minus the binding energy of the electron to the atom. Binding energies of electrons in various shells are different and X-ray photons can ionize inner-shell electrons. Absorption of photons by photoelectric effect is the most important mode for low energy (long wavelength) photons, especially when the energy is just sufficient to eject an electron from a particular shell of the atoms in the medium. This mode of interaction is shared by photons of low energy, including those in the UV region.

Regarding the Compton effect, we need to go back a few decade to review the study of light scattering. Drude, Lord Rayleigh, Raman, Thomson, Debye, and others, have studied the light scattering. They found that

1. the scattered radiation had the same wavelength as the primary rays,

1. 90-degree scattered rays were polarized.

Feynman Diagram forthe Compton Effect

However, when A.H. Compton (1926) and his collaborators studied X-rays scattering, they found the wavelength for the scattered rays a little longer than the original X-rays. The amount of lengthening depended on the wavelength and the angle of scattering. They did not find any polarization. When a photon transfer part of its energy to an electron, it is scattered off from a different direction. Its wavelength becomes longer. The process is equivalent to inelastic collision between photons and electrons. Compton concluded that inelastic scattering begin to appear for photons with energy greater than 0.51 MeV. This process is now known as the Compton effect, by which a photon transfers part of its energy to an electron, and the photon becomes less energetic, resulting in a longer wavelength or lower frequency.

Suppose the spectrum of a X-ray beam consists of a single peak. The spectrum of the scattered X-rays at a particular angle consists of two peaks, one with frequencies of the scattered original photons, and one with longer wavelengths. The relative intensities of the two peaks depend on energies of the photon, and the material used. When photons are scattered through an angle , the wavelength increased by an amount , which depends on

= o(1 - cos)

where o is the original wavelength. The amount is now called the Compton Wavelength.

Dirac postulated the existence of antiparticles, and sort after Anderson (1932) discovered the antiparticle of electron called it positron. A positron and an electron annihilate each other converting to two photons. Not exactly the reverse of annihilation, but at the vicinity of an atom, a photon creates a positron and an electron at the same time from a common center. This production of a particle-antiparticle pair is known as pair production. Pair productions happen for photons with energies greater than (2 x 0.51 MeV =) 1.02 MeV. A single photon disappears, converting to a pair of particle and antiparticle. Due to the law of conservation of momentum, a third body must be present for the pair production. The threshold energy (1.02 MeV) corresponds to the rest mass of an electron-positron pair. The residual energy (h - 2 me c2) is distributed between the kinetic energies of the pair with only a small fraction going to the nuclear recoil.

The pair production can also occur in the field of an atomic electron, to which considerable recoil energy is thereby imparted. Applying the Born's first approximation, it has been shown that photons with 2.04 MeV or more will undergo such a transformation. In the pair production process a pair of particles are produced from a bundle of light energy (one photon). This is not the reverse of the annihilation mechanism between a positron and a beta particle, in which two photons are produced.

Photons with less than 1 MeV energies lose their energy mostly by photoelectric process. Photons with energies between 1 and 5 MeV lose their energies mainly by Compton scattering. Photons with energies higher than 5 MeV lose their energy by pair production. Of course, the three processes compete with one another. Photons with energy with 1 MeV have higher probability of losing energy due to inelastic scattering than photoelectric effect, and the photoelectric probability increases as their energies decrease. The domains of the major processes are displayed in the diagram here. As the photon energy increases, the dominant process shift from photoelectric, to Compton, and to pair productions. The photoelectric effect never competes with pair production.

Pair production is now routinely used to produce positrons and electrons for synchrotrons. Using the same process, protons and antiprotons are also produced.

A beam of rays passing a medium loses energy by all three mechanisms: photoelectric, Compton and pair productions. Regardless of the mode of interaction, the absorption of -rays is by chance. The rate of absorption per unit length, (-dI/dt) is proportional to the intensity, I, itself. The reduction of -ray intensity follows the equation

Interaction of Photons with Matter

1 5/ MeV

Pairproduction

Photo-electric

Compton scattering

Intensity of Parallel Gamma Rays as aFunction of Absorber Thickness.

Thickness x

Intensity, I

where a is the absorption coefficient. Expressed in another form, the intensity I is reduced exponentially as a function of the thickness x of the medium:

I = I0 e – a x

where I0 is the initial incident intensity. The variations of monoenergetic gamma ray (all photons have the same energy) intensity as a function of the thickness x is shown here. The larger the a, the faster the decline of the intensity. Substances containing heavy elements such as lead and lead glass having high absorption coefficient a are excellent absorbers of X-rays and gamma rays.

Review Questions

1. Evaluate the wavelengths of photons whose energies are 1 meV, 1 eV, 1 keV, 1 MeV, and 10.0 MeV respectively. What regions do these photons belong in the electromagnetic radiation spectrum?

2. Describe the photoelectric effect.

3. Describe the pair production process.

4. Describe the Compton scattering of rays.

5. Why lead sheets and lead glass are used as shield for gamma ray radiation?

Interaction of Neutrons with MatterNeutrons are heavy, uncharged particles, and they interact with electrons weakly due to the magnetic moment present in both electrons and neutrons. Collisions between neutrons and atomic nuclei are rare events, because both are tiny compared to the atoms. In elastic collisions, the neutrons do not lose any energy. In inelastic collisions, kinetic energy is transferred between neutrons and the atomic nuclei. Neutrons lose their energies in inelastic collisions with the atomic nuclei, not with the electrons. In cases where the neutrons transfer energy to the atomic nuclei, one or more of the nucleons are excited to a higher level. The excitation energy may be emitted as gamma rays.

What interactions will neutron have with material?What type of material is effective to slow neutrons?How can neutrons be detected?

Neutrons cannot be detected directly from their interactions with matter. However, neutrons are detected due to nuclear reactions induced by neutrons. For example, a nuclear reaction induced by neutron first observed is the reaction with nitrogen:

14N + n 11B + ,

in which case, the tracks due to the particles were observable (Chadwick, 1935). Since boron nuclei absorb neutrons readily, a common neutron detector makes use of the reaction,

10B + n -> 7Li + .

A detection chamber is usually filled with gaseous boron trifluoride, BF3, with enriched 10B. The detector gives out signals due to particles.

After having received the kinetic energy from a fast neutron in an inelastic collision, the nuclei have the ability to cause ionizing of other atoms, causing further excitation and ionization in the media. Since such collision is rare, the density of ion pair is very small. Thermal neutrons have energy levels similar to the kinetic energy of atoms in the medium, and they cause much less ionization, if any.

Neutrons lose very little energy per collision when they collide with heavy nuclei. Nuclei of hydrogen and neutrons have approximately the same mass. In collisions with hydrogen nuclei, neutrons can transfer almost all their kinetic energy to the hydrogen nuclei. Thus, hydrogen-containing compounds such as H2O, paraffin wax, and hydrocarbons (oil and grease) slow down neutrons rapidly.

Biological systems contain a high percentage of water, and water is an effective neutron moderator. Fast neutrons quickly become thermal neutrons in a biological system. Thermal neutron capturing reactions take place even when biological materials are exposed to fast neutrons.

We have extensively discussed nuclear reactions induced by neutrons in the chapters on Nuclear Reactions and on Fission Reactions. A summary is given below. The first two reactions take place in nuclear reactors, whereas the (n, p) and (n, ) reactions produce radioactive isotopes. Boron, B, absorbs neutrons readily, and its reaction is often used for the detection of neutrons.

1H + n 2D + (capture or n, )238U + n 239U + (n, )14N + n 14C + p (n, p)35Cl + n 35S + p (n, p)35Cl + n 32P + (n, )200Hg + n (10 MeV) 197Pt +

197Pt 197Au + 200Hg + n (10 MeV) 198Au + p

198Au 198Hg +

Web Sites About Neutron DetectorUltra High Sensitivity Fission Counter (UHSFC):

http://www.ic.ornl.gov/HTML/ic94130.htmlROMASHKA - multipurpose instrument for measuring neutron cross sections, neutron resonance parameters and gamma-multiplicities in interactions of neutrons with nuclei (with nice diagrams): http://nfdfn.jinr.dubna.su/flnph/usersgui/romash.htm

Review Questions

1. Aside from neutron induced reactions, how do neutrons interact with atoms and molecules in a medium?

2. What neutron reaction is commonly used for detecting neutrons?

Radiation Detectors Radioactivity was discovered from images left on silver bromide photographic plates. New particles were discovered from the study of their tracks in hydrogen bubble chambers and cloud chambers. Ionization of radiation was inferred from their discharging of electroscopes. Photographic plates, bubble chambers, cloud chambers, and electroscopes are radiation detectors. In this section, we shall discuss the principles of these and some other detectors. Most detection methods are based on the ionization in the medium.

Ionization ChamberIonizing radiation produces ion pairs in a gas, and the ion pairs do not recombine until the energies of the electrons have dissipated. Thus, there are positive ions and negative electrons in a gas medium when exposed to radiation.

How can ionizing radiation be detected?How do ionizing radiation detectors work?

In a gas, ions and electrons move freely as do the gas molecules. If we place two electrodes connected to a battery in the medium, the electrodes afford an electric field, which causes the electrons to drift towards positive electrode, and the positive ions towards the negative electrode. Such an arrangement is ionization chamber for the detection of radioactivity

When the ionization chamber is exposed to a source of ionization radiation as shown here, the drifting of electrons and ions will make the detector chamber a conductor. Thus, a current is registered on the ampere-meter. The ionization chamber is a simple detector for radioactivity.

An ionization chamber is a little more sophisticated than an electroscope for the detection of radioactivity. Rutherford placed a thorium oxide (ThO2) sample directly in the detector chamber. He noticed that the radioactivity increased with time after a sample was just put in. After removing the sample carefully without changing the air in the chamber, he found the air remained radioactive. The radioactive air decayed with a specific half life. Other radioactive samples did not give the same observation. His experiment suggested the existence of a radioactive gaseous element. The experiment was later interpreted as due to the decay of Th (, ) Ra (, ) Rn. Several isotopes of Th produce radon isotopes in their decays.

Key Components in a Simple Ionization Chamber

–+–+–+–+–+

+

–

Ampere-meter

Detectorchamber

Ionizingradiation

Battery

Loadresister

Of course, one uses the most sensitive ampere-meter in setting up the ionization chamber. The current registered in the ionization chamber is proportional to the number of ion pairs generated by radioactivity. Thus, the higher the radioactivity, the higher the current. Ionization chambers quantitatively measure radioactivity. The voltage supply enables the electrodes to collect electrons and ions, but the current is mainly determined by the number of free electrons in the chamber, not on the voltage. However, depends on the electrode arrangements and chamber geometry, the voltage must be sufficiently high for effective collection of electrons.

Review Questions

1. How does an ionization chamber work? What are the key components in the ionization chamber?

2. What are the isotopes of Rn from decays of 227Th, 228Th, 230Th? Which isotopes of Rn has the shortest half life? (The merit of this exercise is to know how to find information in problem solving.)

Proportional CounterDiscovery is an important goal of scientific research, and methodologies for doing research are constantly under development. Soon after getting ionization chambers to work, improvements are made. The improvement in the instrumentation leads to new phenomena, making research and development an interesting adventure.

How can the sensitivities of ionization chambers be improved?What happens when the voltage is increased?

At some hundreds volts, the improvement in sensitivity is more than collecting all the When voltages applied to electrodes of ionization chambers increase, the sensitivities increase. electrons and ions on the electrode. The currents corresponding to multiples of ions and electrons produced by radioactivity. To distinct them from simple ionization chambers, these detectors are called proportional counters.

Gas Multiplication

–+

–+–+–+

–+–+–+–+–+–+–+–+–+

–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–+–

+–+–+–+

In proportional counters, the high voltage applied to the electrodes created a strong electric field, which not only collect but also accelerate electrons. The energies acquired from the electric field by electrons accumulate and they are used to ionize other molecules, producing secondary ion pairs, initiating an avalanche of ionization by every a single electron generated by radiation. Such a process is called gas multiplication.

It should be noted, however, that the small mass and high energy of electrons make them drift 100,000 times faster than ions. Thus, the current is mainly due to the drifting electrons with only a small fraction due to the drift of ions.

Despite the multiplication due to secondary ion pairs, the ampere-meters register currents proportional to the numbers of primary electrons caused by radiation entering the detectors. Thus, currents of proportional chambers correspond to amounts of ionization radiation entering the proportional chamber.

When voltages applied to proportional counters get still higher, sparks jump (arcs) between the two electrodes along the tracks of ionizing particles. These detectors are called spark chambers, which give internal amplification factors up to 1,000,000 times while still giving an initial signal proportional to the number of primary ion pairs.

Review Questions

1. How does an ionization chamber work?What are the key components in the ionization chamber?

2. Assume that 35 eV is required to create an ion pair. If the applied voltage is 200 V, what is the amplification factor for the proportional counter?

Geiger-Muller Counters Perhaps the most widely used radioactivity detectors are Geiger-Muller (often called Geiger) counters. More precisely these counters detect numbers of ionization particles entering the detector. Unlike the ionization chambers or proportional counters, Geiger counters do not reveal numbers of primary ion pairs in their detecting chambers.

What is the working principle of Geiger-Muller Counters?

Geiger-Muller counters evolve from proportional counters. When the voltages applied to the ion chamber of the ionization chamber reach more than 1,000 V, as few as one primary ion pair in the chamber causes a spark (arc). Whenever an ionization particle (including photons) enters the chamber, a primary ion pair causes a single spark. The charges jumped over the electrodes depend on the number of primary ion pairs, but we often are more interested in the numbers of particles entering the chamber.

A spark causes a temporary conduction in the detector chamber. The voltage across the two electrodes drops during the sparking period, but a current flowing across a resister causes

the voltage between points on both sides of a resister to increases (V = i R). The sudden drops or increases in voltage are called pulses. Geiger counters count the number of pulses, and this can easily be achieved by electronic means. The counters can also be designed to give an audible signal for each pulse.

A Geiger counter usually refers to an instrument consisting of a detector, a high voltage supplier, and an electronic pulse counter. Usually, audio and meter outputs are parts of an instrument. When the audio output is switched on, the Geiger counter gives a clicking sound whenever a pulse is registered. The frequency of the clicks is proportional to the radioactivity (Bq) of the source. The meter output is very similar to an ampere-meter. The current is proportional to the frequency of the pulses, however, not related to the energy of the particles entering the detector.

Geiger-Muller counters count the number of radiation events, not the energy of the ionizing particles. At this level of operation, the number of counts per unit time from a steady source is independent of the voltage applied to the electrode. To insure the stability and uniformity of the detector, a voltage in the middle of a range of voltages that gives a steady number of counts from a steady radiation source is usually chosen.

Geiger-Muller counters are usually used to detect X-, gamma- and beta-rays. Alpha particles have a limited range, and they may not be able to enter the chamber to cause any ionization of the gas in it. Thus, alpha particles may escape detection by Geiger-Muller counters.

Due to their high sensitivity, Geiger-Miller counters are useful for geological survey, personnel monitoring, tracking of radioactivity movement, and radioactivity detection. The frequency of clicks is proportional to the radioactivity of the source, and the audio output frees the visual sense for other purposes. However they can not differentiate sources

Working Components of a Geiger Muller Counter

1500 Vsupplier

– +

Detector

Source

Geiger-Muller Counter:Pulse counting electronics

from -ray sources, and other detectors are required for proper characterization of radioactivity.

Geiger counters count pulses. After each pulse, the voltage has to return to a certain level before the next pulse can be counted. Thus, after each pulse, there is a period called dead time during which radiation can not be detected. The length of the dead time depends on the gas mixtures used in the detector, and on the sophistication of the electronics. When the source has a very strong radioactivity, the pulses generated in the detectors are very close together. As a result, the Geiger counter may register a zero rate. In other words, a high radioactive source may overwhelm the Geiger counter, causing it to fail. When you use a Geiger counter for a survey, keep this in mind. The zero reading from a Geiger counter provides you with a (false) sense of safety when you actually walk into an area where the radioactivity is dangerously high.

Ionization chamber, proportional counter, spark chamber and Geiger-Muller counters are similar in design and construction. Different voltages applied to the detector chambers make them perform differently. Depending on the applied voltage, the characteristic of the detector changes.

Review Questions

1. How does a Geiger-Muller counter work? What are the key components in a Geiger counter?

2. Why there is a dead time in Geiger counters? What caution should be exercised in using Geiger counters for survey work?

Solid-state DetectorsSolid-state detectors are for accurate measurements of radiation energy. They are based on ionization, but they are very different from ionization chambers, proportional counters, spark chambers and Geiger counters.

What solids are used for solid-state detectors?How do solid state detectors work?

Semiconductors such as silicon and germanium are used for solid state detectors. Every atom in the crystal is bonded to four other atoms throughout the entire crystal. However, usually doped semiconductors are used as detectors. Signals in solid states after receiving ionization radiation are processed by electronic means.

Dead Time in Pulse CountingDead time

In a solid semiconductor, atoms are fixed in their locations. Electrons are tightly bound to atoms or chemical bonds. Pure semiconductors have some free electrons and holes due to thermal motions or defects. Electrons are negative charge carriers, whereas holes are positive charge carriers. Both electrons and holes are responsible for the small conductivity of semiconductors, but movement of hole is much slower than that of electron in a solid.

Energy required to free an electron from the valance band into the conduction band is called the band gap, which depends on the material: diamond, 5 eV; silicon, 1.1 eV; germanium, 0.72 eV. At room temperature, the thermal energy gives rise to 1010 carriers per cc. At liquid nitrogen temperature, the number of carriers is dramatically reduced to almost zero. At low temperature, it is easier to distinguish signals due to electrons freed by radiation from those due to thermal carriers.

Doping semiconductors is a process by which some atoms of the crystal are replaced by other type of the atoms. For example, atoms of a germanium crystal are replaced by atoms of phosphorus. A phosphorus atom has one more electron than the host atoms, and the phosphorus doping adds negative carriers in the crystal creating a negative (N) junction. Similarly, doping with impurities deficient in electron adds positive carriers to the region, forming a positive (P) junction. Solids with a N or P junction is called a diode, and those with both a N and a P junction are called transistors. Electrons and holes in transistors do not belong to particular atoms. They belong to either the valence band or the conduction band. Electrons in the conduction band move easily under the influence of an electric field.

The electronics used to analyze the pulses does more than counting. It separates the pulses into hundreds of groups called channels according to the pulse heights. Therefore, the equipment is often called multi-channel analyzer. When intensities of these channels are displayed according to their energies, the measurement gives a spectrum. A gamma-ray spectrum of 56Co measured using a solid state detector is shown above. The continuous background is due to Compton scattering. Single and double escape peaks (marked SEP and DEP) are also shown.

The modern instruments for X-ray and gamma ray detection use doped solid detectors. A P-N junction of semiconductors is placed under reverse bias, thus no current flows. Passage of ionizing radiation through the depleted region excites electrons into the conduction band, causing a temporary conduction which gives rise to a pulse corresponding to the number of excited electrons or energy entering the solid state*.

* Low level radiation sensor seeking industrial collaborators to develop and commercialize future low-level radiation sensor systems: Germanium detector provides high-resolution data has been developed. See web site: http://www.llnl.gov/sensor_technology/STR11.html

Gamma ray spectrum of 207mPb (half-life 0.806 sec)

207mPb Decay Scheme

13/2+____________1633.4 keV-1e5

1063-1e4 569 5/2-____________569.7 keV 1063-1e3 . . 569 1/2-____________0.0 stable-1e2 -10 569 + 1063

-1

Review Questions

1. What are semiconductors? What elements are used to dope semiconductors to make N and P junctions?

2. What advantages do solid state detectors have over proportional and Geiger counters?

Scintillation Counters and Fluorescence ScreensScintillation counters are commonly used for X-rays and gamma rays. The name suggests that the working principle for scintillation counters is not based on ionization, but based on light emission.

What is the working principle of scintillation counters?

Photons striking a sodium iodide (NaI) crystal, which contains 0.5 mole percent of thallium iodide (TlI) as an activator, cause the emission of a short flash of light in the wavelength range of 3300-5000 A (in the ultraviolet region). The light flashes are detected by a photomultiply tube, which gives a pulse corresponding to the light intensity. These pulses are measured by a multi-channel counter.

The Key Components of a Typical Scintillation Counter

High voltagesupplier andmulti-channelanalyzer /computersystem

Photomultiply tube

Photo-cathode

Na(Tl)Icrystal

Thin Alwindow

X- or rays

The output pulses from a scintillation counter are proportional to the energy of the radiation. Electronic devices have been built not only to detect the pulses, but also to measure the pulse heights. The measurements enable us to plot the intensity (number of pulses) versus energy (pulse height), yielding a spectrum of the source.

Scintillation counters and solid state detectors are used to determine the energy of the incoming particles. The former uses a doped NaI crystal, which may be kept at room temperature, and needs no special care. Most solid-state detectors must be maintained at low temperatures (cooled by liquid nitrogen or liquid helium) to achieve excellent resolution, i.e., to distinguish radiation particles of various energy. Pulses from solid-state and scintillation detectors are counted by multi-channel analyzers or computers. Each measurement gives a spectrum of the source of radiation.

Review Questions

1. How does a scintillation counter work?What does it measure and what type of results is obtained.

2. What are the advantages of solid-state detectors and scintillation counters for radiation measurement?

Fluorescence ScreensJ.J. Thomson used fluorescence screens to see electron tracks in cathode ray tubes. In 1895, Röntgen saw the shadow of his skeleton on fluorescence screens. His screen was made of barium-platinocyanide. Rutherford observed alpha particle on scintillation material zinc sulfide, ZnS. Fluorescence screens are important detectors for ionizing radiation and high energy photons.

Fluorescence material absorbs invisible light and the energy excites the electron. De-exciting of these electrons results in the emission of visible light. By mixing different materials together, we have engineered many different fluorescence materials to emit lights of any desirable colors.

Fluorescence screens are convenient detectors of high-energy radiation. They are used in many other applications such as fluorescence tubes, UV detectors, computer and TV screens and movie screens. Even laundry detergents contain fluorescence material to emit blue light to make the cloth whiter than white after washing with them.

Review Questions

1. What is a fluorescence material?Give some applications of fluorescence material.

2. How do TV screens work?

Cloud and Bubble ChambersStudies of particle tracks have led to the discovery a zoo of particles. Cloud and bubble chambers have contributed greatly to these discoveries. These chambers show tracks of ionizing particles.

Why do cloud and bubbles form along the trail of these particles? Where did the ideas of using cloud and bubble chambers to record the tracks of particles come from?

Cloud and bubble chambers for the detection of radiation particles are based on the ionization effect of energetic particles. However, working functions for cloud and bubble chambers are different from ionization chambers, proportional and Geiger counters.

The ion pairs on the tracks of ionizing radiation form seeds of gas bubbles and droplets. Formations of droplets and bubbles provide visual appearance of their tracks. Therefore, cloud and bubble chambers are called path-, 3-dimensional-, or track-detectors. In the good old days, photographs of these tracks were taken for detailed analyses. In modern science, high-energy particle track detectors are built using sophisticated electronics and computers for the study of particle behavior.

The story on the development of cloud chambers is fascinating because the chambers were originally studied for a completely different reason than the study of radiation. Furthermore, a young man at his teens initiated the studies.

At age 15, the Scottish physicist C.T.R. Wilson (1869-1959) spent a few weeks in the observatory on the summit of the highest Scottish hill Ben Nevis. He was intrigued by the color of the cloud droplets. He also learned that droplets would form around dust particles. He built apparatus according to an earlier study of Coulier and Aitken to expand moist air to study the formation of cloud. Between 1896 and 1912, he found dust-free moist air formed droplets at some over-saturation points. He repeated the experiments with the same air and found cloud drops always form at some saturation points. He concluded that although dust particles were nucleation centers of cloud drops, there was something else that would also nucleate cloud drops. His meticulous experiments showed that these centers were always present in air, and he considered them ions rather than dust particles. He further suspected that these ions were produced by energetic particles, and he was determined to confirm that.

The news of Röntgen's discovery reached Wilson, who also learned of J.J. Thomson's investigation of air conductivity due to X-rays. He set up his cloud chamber apparatus in front of an X-ray tube, and after the X-rays were turned on, he expanded the air in the chamber. To his astonishment, he found many cloud-like small drops, not the rain-like large drops as he usually saw. The X-rays have created a large number of cloud nucleation centers. This marked the beginning of his research in trying to perfect an apparatus for the detection of ionizing particles. He carefully designed the apparatus so that the expansion

Photographing the Particle Tracks

Cloud or bubble chamber

radiation

will not disturb the air, leaving the tracks of ionizing radiation undistorted. This apparatus enabled scientists to study tracks of radiation. Moreover, the tracks marked by cloud-like droplets can be seen, photographed, studied, reported, and published.

The perfection of the cloud-chamber techniques had a much farther impact in the development of nuclear science and particle physics. Later using oil vapors, Milikan studied the force exerted on a drop by an electric field, and determined the amount of a fundamental charge (of an electron). Cloud chambers showed -particle tracks being fatter and shorter than those of particle, and they enabled scientists to study behavior of particles under the influence of electric and magnetic fields. Tracks in cloud chambers revealed the rays (electrons ejected by particles), origins of secondary electrons, ranges of and particles, variations of ionization along the tracks, charge densities of ionization, and absorption of X-rays by atoms.

Using the cloud-chamber technique, Compton discovered that high energy photons gave portions of their energies to electrons, and they became less energetic with longer wavelength. This is now known as Compton scattering. Compton and Wilson shared the 1927 Nobel prize for physics. Furthermore, using the cloud chamber while working as Rutherford's student, P.M.S. Blackett (1897 - 1974) studied elastic collisions of particles with atoms, and transmutation of nitrogen when bombarded by particles, 14N (, p) 17O. The tracks were fatter than the proton tracks, and the angles of deflection agreed with his calculated results. Blackett attached Geiger counters on both sides of large cloud chambers to catch the tracks of elusive cosmic rays. This further development led to other achievements including Anderson's discovery of positrons, and the visual demonstration of the processes of pair production and annihilation of electrons and positrons. Blackett (1948) received the 1948 Nobel prize in physics "for his development of the Wilson cloud chamber method, and his discoveries therewith in the fields of nuclear physics and cosmic radiations". The cloud chamber contributed to the discovery of the transmutation of atomic nuclei carried out by Cockroft (1951) and Walton (1951). Rutherford once remarked that “the cloud chamber was the most original and wonderful instrument in scientific history.” The cloud chamber had been evolved into a continuously sensitive detector by diffusing warm vapor into a cool chamber.

Like the formation of droplets from saturated vapor, the formation of bubbles in a liquid also requires nucleation, without which overheating results. Ion pairs due to radiation serve as nucleation centers, and the tiny bubbles mark their tracks in bubble chambers, which were developed by the U.S. physicist Donald A. Glaser (1926-). He began his research in elementary particles, some of which had energy in the order of GeV (109 eV), and the diffusion cloud chambers he constructed could not covered the entire tracks. In order to keep the chambers to a reasonable size and yet covered the entire track, Glaser (1960) thought of using a superheated liquid to observe the entire track of his particles. He contributed to both the theories of bubble nucleation and engineering of instruments. Among the liquid he had used were diethyl ether, propane, xenon, and hydrogen. The idea of using bubble chamber was quickly adopted by others. The success of the bubble chambers is marked by the discovery of a large number of new particles and phenomena. Precise information on masses, spins, lifetimes, parity, and decay had been determined. The

importance of these developments was highlighted by the Nobel Prize for physics awarded to him at age 34 (in 1960). The citing of the prize was for his invention of the bubble chamber.

Tracks of single particles and their decay products have been recorded in bubble chambers. For example, when an antiproton, p , entered a propane bubble chamber, it underwent a charge exchange reaction with a proton, p, to give a neutron, n, and an antineutron ,

p + p + n(charge exchange)

A moment later, the antineutron annihilated with another neutron giving a star of tracks due to the many particles in the reaction. Agnew et al., (1958) suggested the five tracks to be due to + and - pions in the reaction,

+ n 3+ + 2–.

A sketch of the tracks as seen in a propane bubble chamber is shown here. The pions have a mass of about 140 MeV, and a life time of 2.6 x 10-8 s. They were discovered by Cecil F. Powell and his co-workers in 1947. The discovery of pions in the cosmic radiation used yet another track detectors using photographic emulsions, which will be discussed in the next section.

Millions of particle-track photographs have been taken using the bubble chambers for the study Each photograph contains many tracks, and each has to be analyzed. Almost all tracks are left by particles already well known and understood. The few tracks of new particles are buried in trillions of tracks. Their discoveries are getting harder as more and more have been discovered.

Review Questions

1. What cause the formation of droplets in clouds?And what causes the formation of bubbles in overheated fluids?

2. Why bubble chambers can cover the entire track whereas cloud chambers can not?

A Sketch of the Tracks of Charge Exchangeand Antineutron-Proton Annihilation.

antiproton

Chargeexchange

Antineutron-neutronannihilation

–

+

Photographic Emulsions and FilmsEveryone knows that when photographic films are exposed to light, the silver bromide grains of the emulsion are sensitized and they developed into blackened grains. From the stories of discoveries of radioactivity and X-rays, you have also learned that photographic emulsions played important in nuclear technology. Yet, we often forget to count photographic films and emulsions are detectors of radiation. In fact, they are two-dimensional detectors. When several films are stacked together to record particle tracks directly, these are three-dimensional detectors. On the other hand, dentists still use films to record X-ray images of teeth.

Photographic films and emulsions of various speed and sensitivity towards light. Special films have been made for X- and -rays. Often auxiliary devices such as fluorescence screens are used in medical applications. When photons of high energy strike the fluorescence screens, visible lights are emitted that give images on the films. Images on film are permanent, and they may be reinvestigated.

An emulsion sensitive to fast moving protons was independently developed by Zhdanov in Leningrad and by Ilford Laboratories in 1935. The method has some success, but it is not widely used because it did not give constant ranges for energy calculation. This is probably due to the consistency of particle size in the emulsion.

Review Question

1. Give some examples where photographic films are used for the detection of ionizing radiation.(Discoveries of X-rays, radioactivity, and many high-energy particles are made via using photographic plates)

Exercises1. Most significant scientific discoveries require instruments for their dectection.

However, instruments alone were insufficient. What are other ingredients for scientific discoveries? Describe some examples of discoveries, including instruments used experiment performed.

2. At 273 K and 1 atm pressure, 1.0 mol of N2 occupies 22.4 L. Calculate the number of N2 molecules in 1.0 L. At 277 K, 1.0 L of water weighs 1.0 kg. Calculate the number of moles of water in 1.0 L. Calculate the number of H2O molecules in 1.0 L at 277 K. The density of lead (Z, 82; at. wt. 207.2) is 11.29 g/mL, calculate the number of atoms in 1.0 L. (1.0 mole of N2 an avogadro's number, 6.02 x 1023, of N2 molecules).

3. Calculate the velocities of the alpha-particle, the proton, and the electron if they all have the following kinetic energies:10.0 MeV, 1.0 MeV, 1.0 keV, 100 eV, and 1 eV.

4. Calculate the ratios of the rates of energy loss (stopping power) for the alpha-particle, the proton, and the electron by using the simple equation:

- (dE/dx) = k (M z2 / E).

Assume these particles have the same kinetic energy.

5. Explain the three processes by which beta particles lose energy when they pass by a nucleus.

6. Gamma-rays lose their intensity exponentially, I = I0 e-a x.where Io is the initial incident intensity, x is the distance in the medium, a is the absorption coefficient, and I is the intensity of gamma-rays after passing the medium by a distance of x. Find the distance required to reduce I to 0.25 I0., express this result in terms of a.

7. For Al (aluminum) and Pb (lead), a = 0.1 and 10 respectively for certain gamma rays. Calculate the ratio of half thickness (i.e., I = 0.5 Io) for these two substances.

8. Describe the mechanisms by which the gamma rays interact with matter. Explain each mechanism separately.

9. Explain how a Geiger-Muller counter works.

10. How do bubble chambers and cloud chambers work? What are the similarities and differences between bubble chambers and cloud chambers?

11. What roles do photographic films and emulsions play for the detection of ionizing radiation?

Reference and Further Reading

Agnew, L.E., Eliot, T., Fowler, W.B., Gilly, L., Lander, R., Oswald, L., Powell, W., Segrè, Steiner, H., White, H., W. Wiegand, C., and Ypsilantis, T. (1958), Phys. Rev. 110, 994.

Brackett, P.M.S. (1948) Cloud chamber researches in nuclear phyusics and cosmic radiation, in Nobel lectures, physics. 3. Published for the Nobel Foundation in 1965 by Elsvier Publishing Company.

Chadwick, J. (1935), Neutron and its properties, in Nobel lectures, physics. 3. Published for the Nobel Foundation in 1965 by Elsvier Publishing Company.

Cockcroft, J.D. (1951) Experiments on the interaction of high-speed nucleons with atomic nuclei, in Nobel lectures, physics. 2. Published for the Nobel Foundation in 1965 by Elsvier Publishing Company.

Walton, E.T.S. (1951) Artificial production of fast particles, in Nobel lectures, physics. 3. Published for the Nobel Foundation in 1965 by Elsvier Publishing Company.

Compton, A.H. (1926), X-rays and electrons, Chap. 9, Nostrand

Compton, A.H. (1927), X-ray as a branch of optics, in Nobel lectures, physics. 2. Published for the Nobel Foundation in 1965 by Elsvier Publishing Company.

Glaser, D.A. (1960), Elementary particles and bubble chambers, in Nobel lectures, physics. 3. Published for the Nobel Foundation in 1965 by Elsvier Publishing Company.

B.G. Harvey, Introduction to nuclear physics and chemistry, 2nd Ed., Prentice Hall, 1969.

Z. M. Haissinsky, Nuclear chemistry and its applications, Addison-Welsley, 1964

Wilson, C.T.R. (1927), On the cloud method of making visible ions and the tracks of ionizing particles, in Nobel lectures, physics. 2. Published for the Nobel Foundation in 1965 by Elsvier Publishing Company.