NUCLEAR PHYSICS -...

SPH3U Nuclear Physics 1

NUCLEAR PHYSICS

1) Radioactivity

The Discovery of Radioactivity Cathode Rays By the middle of the nineteenth century, the properties of electric currents and magnetism were fairly well understood and people were using electricity and magnetism to explore the properties of matter. The actual nature of electricity was unknown since at the time the existence of electrons was unknown. At the time it was believed that the smallest unit of matter was the atom [Dalton, 1808] which was not divisible. Experiments with electricity would show this not to be true. One of the devices being used was the cathode-ray tube. This was a closed glass tube with a metal plate at each end, each of which is connected to a positive or negative terminal of a high-voltage electrical source. It was found that the air in the tube would conduct electricity from the negative plate (cathode) to the positive plate (anode). It was also found that even if the air was removed (with a vacuum pump) current would still flow and the region of the tube near the positive end would glow faintly. It was proposed that this glowing was caused by some rays which were being emitted by the cathode (cathode rays). Further investigation of the cathode rays revealed the following properties; 1) they carried negative electrical charge; negative charge would build up at the glowing end

of the tube

2) their path could be bent by a magnetic field. This also showed that they carried electric charge (it was known that moving electric charges can be influenced by magnets).

3) based on the amount of bending of their path by a magnetic field, the masses of the particles that make up these rays must be about 1/2000 that of the lightest atom (hydrogen) [J.J. Thomson, 1897].

J.J. Thomson concluded that these “rays” were actually fast-moving particles and he named them electrons. He also proposed that they originally came from atoms and were therefore components of atoms (1897). This was the first indication that the atom was made up of smaller pieces.


X-rays; Roentgen In December 1895, Wilhelm Roentgen was experimenting with a cathode ray tube which was covered with black paper (which blocked the glow produced by the cathode rays). He noticed that when the tube was operating, some crystals left near the tube would glow and covered photographic plates would become fogged (as if they had been exposed to light). He concluded that the high energy cathode rays must be giving up their energy when they hit the positive plate and this energy was being emitted as a type of radiation which he called x-rays ( "x" because it was unknown what they were). Roentgen and others determined some of the properties of x-rays; 1) they can pass through many substances

2) they are produced when high speed electrons strike matter

3) they can expose photographic film (cause a chemical reaction in the film)

4) they can cause some materials to glow (fluorescence) They also share some of the properties of light; 1) travel at the speed of light

2) can be reflected and refracted

3) travel in straight lines

4) are not affected by electric or magnetic fields We now know that x-rays are a form of electromagnetic radiation, which is also what visible light is. The properties of penetration and ability to expose film allow us to use x-rays to take photographs of the insides of objects (particularly ourselves). They can also be used to kill cancerous cells. In the early days of investigation of x-rays and construction of more powerful x-ray sources, many researchers were exposed to large amounts of x-rays and suffered injury and even death. Radioactivity; Becquerel and the Curies Fluorescence is a glow that is produced by some materials when they are exposed to x-rays (or other types of radiation) and only occurs while they are exposed. Some materials also glow when they are exposed to sunlight and will continue to glow for a while afterwards – this is called phosphorescence. French Physicist Henri Becquerel [1896] wanted to investigate whether some phosphorescent materials might also be emitting x-rays as well as light after they were exposed to sunlight. He was preparing to do this in February 1896 with a uranium (which was known to be

Wilhelm Roentgen

The first human x-ray – Mrs. Roentgen

http://www.rnrassociates.com/wordpress/wp-content/uploads/2010/11/WILHEL12.jpg


phosphorescent) sample which would be exposed to sunlight then left on a covered photographic plate. If it emitted x-rays, they would be able to penetrate the cover of the plate and expose the film. Unfortunately it was too cloudy that day so he put the materials away in a drawer and they remained there (not exposed to light) for the next four days because of continued cloudiness. Tired of waiting for good weather, Becquerel decided to develop the photographic plate anyway. He was amazed to find that it had been exposed by the uranium, even though the uranium hadn't been made to phosphoresce by sunlight. Somehow, the uranium was emitting something even though it hadn't been stimulated by sunlight. This was the discovery of radioactivity: the spontaneous emission of rays from the atoms of certain elements (they were originally called Becquerel rays). Becquerel The nature of radioactivity was further investigated shortly afterwards by Marie Curie and her husband Pierre. They found that the amount of radioactivity that a substance emits depends only on how much substance there is. It does not depend on things like the temperature of the substance, electric or magnetic fields, or chemical reactions that the substance experiences. By examining the ore from which uranium is extracted (pitchblende), they were able to discover two new chemical elements; polonium and radium [1898]. The residue of the pitchblende was still radioactive after all the uranium was removed, indicating the presence of other unknown radioactive elements. Many elements have since been discovered to be naturally radioactive, while others are not radioactive. In 1903 Becquerel and the Curies were given the Nobel Prize in Physics for discovery of radioactivity. In 1911 Marie Curie was given a second Nobel Prize in chemistry for discovery of polonium and radium (the only person to ever win two in science). Many of the early researchers in this field suffered serious ill effects from the radioactivity. Marie Curie showed signs of radiation sickness when she died, and over 100 people probably died due to overexposure to radiation in the 20 years following the discovery of radioactivity.

The Nature of Radioactive Emissions

Alpha, Beta, and Gamma rays Continued investigation of radioactivity revealed that the emissions from radioactive substances come in different types. These types were distinguished by how easily they penetrated other materials as well as by how they behaved in magnetic fields. An electrically charged object moving in a magnetic field will experience a sideways force and its path will be bent, and the amount of bending depending on the electric charge and mass of the object.

Rutherford

The Curies


Much of this work was done by Ernest Rutherford at McGill University in Montreal (1900). Rutherford put a small amount of radium in a lead box with a small opening in it. By setting up a magnetic field in the region outside the box he was able to show that some of the rays were bent one way, others were bent the opposite way (showing that they had the opposite charge), and some passed straight through the magnetic field (showing they had no charge). These different types of radiation

were named Alpha (), Beta (), and Gamma () rays. These particles were found to have different properties.

Alpha particles () ;

1) an alpha particle is the nucleus of a helium atom (2 protons and 2 neutrons)

2) they have a positive electric charge (value: +2)

3) alpha particles can penetrate only a few centimeters of air before being absorbed, or are easily stopped by a thin sheet of aluminum foil

Beta particles ();

1) beta particles are high-speed electrons ejected from the nucleus of an atom (not the electron cloud orbiting around the nucleus)

2) they have a negative electric charge (value: –1)

3) beta particles can penetrate about 50 cm through air and a few millimeters of aluminum before being stopped

Gamma rays ();

1) gamma rays are electromagnetic rays (similar to light or x-rays) with extremely high energy

2) they have no electric charge

3) they travel at the speed of light, and have no mass

4) gamma rays can penetrate up to 30 centimeters of lead and 2 km of air before being absorbed


2) Atomic Structure and the Nucleus

The Atomic Theory of Matter Dalton's Atomic Theory John Dalton devised the first atomic model of the structure of matter [1810]. The main ideas of this model are:

• matter is made of small indivisible particles (called atoms) • atoms of the same element are identical • each element is characterized by the mass of its atoms • atoms combine to form chemical compounds

Thomson's Atomic Model When Thomson discovered that cathode rays were electrons, he reasoned that they must be coming from the atoms in the cathode and therefore the atoms must be divisible. He also reasoned that the atoms must be electrically neutral so there must also be some positive charge present in each atom. In 1904 he suggested that the atom was a positively charged sphere with negatively charged electrons embedded in it (the electrons balancing the charge of the positive sphere and held to it by electrostatic attraction).

The Discovery of the Nucleus Rutherford, Geiger, and Marsden In 1911 Rutherford (working at the University of Manchester) designed and performed an experiment to probe the structure of the atom. The work was performed by two of his students, Geiger and Marsden. The apparatus was set up as shown in the diagram. A source of alpha particles was placed inside a lead container with a hole which allowed a beam of alpha particles to be emitted. This beam of particles was then aimed at a thin piece of gold foil. Since the atoms were electrically neutral and the alpha particles had a positive charge, the alpha particles should pass straight through the gold foil without interruption or with only a slight deflection. The alpha particles could be detected by the radiation they produce when they strike a fluorescent screen. It was found that most alpha particles did travel through the foil, some deflected slightly, but others were deflected by very significant amounts. Some even bounced almost straight back.


Rutherford said it was like firing a shell at a piece of tissue paper and having it bounce back toward you! The only way such large deflections could have happened was if the alpha particles were being repelled by a small, strongly concentrated, region of positive charge (since the alphas are also positive). Rutherford proposed that the positive charge in an atom was concentrated at the centre and he named this region the nucleus, and the electrons orbited in the empty space around the nucleus. The size of the nucleus was about 1/10,000 the size of the whole atom (defined by the

electron cloud). A typical size for an atom is 1010 m and the nucleus is about 1014 m in diameter. Rutherford knew that the hydrogen nucleus had the smallest amount of positive charge so he named it the proton. He said that the nucleus of other atoms with more charge would be made up of more protons. It was realized that the masses of the other nuclei were too large to be accounted for by protons alone so another particle, the electrically neutral neutron was proposed to account for the discrepancy. This led to our current understanding of the broad structure of the atom. The neutron was eventually discovered by James Chadwick in 1932.

The Structure of the Nucleus: Isotopes The number of protons in the nucleus of an atom determines which chemical element it is. This is represented by the atomic number of the element (symbol: Z). The number of electrons moving around the nucleus also equal to Z (when it is electrically neutral). The total number of neutrons and protons in the nucleus is the atomic mass number (symbol:

A). The number of neutrons (N) is then given by N = AZ. Protons and neutrons are also known as nucleons. Thus, the mass number is the number of nucleons in the nucleus.

The symbol used to describe the nucleus of an atom of element X is written as: XAZ

For example, O168 represents the nucleus of an oxygen atom with 8 protons and 8 neutrons. It

is also referred to as oxygen-16. The symbol for copper-64 would be Cu6429 which has 29 protons

and 64−29=35 neutrons. The masses of atoms are often expressed in atomic mass units (u). The atomic mass unit is

based on the mass of a carbon-12 atom, which has a mass of 1.99265 1026 kg. One u is

defined as 1/12th of the mass of a carbon-12 atom so 1 u = 1.66054 1027 kg. The mass of an atom (expressed in atomic mass units) is usually close to its atomic mass number. For example, helium-4 has a mass number of 4 and a mass of 4.0026 u.

Rutherford Model


The masses of the fundamental particles in atomic mass units are: neutron: 1.00866 u

proton: 1.00728 u electron: 0.000548580 u

Many elements have nuclei that can have differing numbers of neutrons (recall: the number of protons must be the same for atoms of the same element). These are different isotopes of the same element. For example, hydrogen has several naturally occurring isotopes. Different isotopes of the same element react the same way in chemical reactions and make the same compounds. For example, in “heavy water”, the hydrogen atoms are deuterium atoms.

Isotopes of Hydrogen

hydrogen : H11 (or hydrogen-1, also known

as protium) mass: 1.0078

deuterium: H21 (or hydrogen-2, also known

as heavy hydrogen) mass: 2.0141 u

tritium: H31 (hydrogen-3)

mass 3.0160 u

Two isotopes of oxygen are oxygen-16 ( O168 ) and

oxygen-18 ( O188 ). Oxygen-16 is much more

common than oxygen-18, but they can both form compounds with other atoms in exactly the same way because they have the same number of electrons orbiting the nucleus. When referring to an isotope like uranium-235 (shortened to U-235), the numerical part of the name (in this case 235) is the atomic number of the particular isotope that we are dealing with. The atomic masses of isotopes which have more neutrons are larger than the mass of those with fewer neutrons. The mass that is usually quoted in chemical periodic tables is either the mass of the most common isotope, or a weighted average of the masses (which takes into account the fact that some isotopes are more common than others). Since one isotope is usually much more common than the others, the atomic mass is usually fairly close to that isotope’s mass. For example, in naturally occurring hydrogen gas, 99.985% is hydrogen-1, and 0.015% is deuterium, and there is virtually no tritium. For many elements, some of the isotopes are stable but others are radioactive (e.g. tritium). The radioactive ones are known as radioisotopes. Atoms of a particular radioisotope can spontaneously change into other particles by radioactive decay.


3) Radioactive Decay

Transmutations During his experiments with radioactivity, Rutherford realized that the particles that are given off by radioactive materials are coming from the nuclei of the atoms that make up the substance. This emission of particles from a nucleus is called radioactive decay. Rutherford realized that the decay of a nucleus means there is a change in the nature of the nucleus. The nucleus can change from one element to another while emitting the radiation. This change in the type of nucleus is called transmutation. In a transmutation, the original nucleus is called the parent nucleus, and the resulting nucleus is the daughter nucleus.

Alpha () Decay In alpha decay, the parent nucleus changes into the daughter nucleus and ejects an alpha particle (a helium nucleus). This means that the daughter nucleus will have two fewer protons and two fewer neutrons than the parent. The total mass number and atomic numbers are the same before and after the transmutation: no particles are lost. The daughter nucleus has an atomic number 2 less than the parent and an atomic mass number 4 less than the parent. For example, radon-222 decays to polonium-218:

Radon Polonium + alpha

Radon has 86 protons and Polonium has 84. We can describe the alpha particle using the same notation as used for the nucleus. The symbol for an

alpha particle is He42 (since it is the same as a helium

nucleus).

The above -decay can be written as He Po Rn 42

21884

22286 .

Note that the atomic numbers balance (86 = 84+2) and the atomic mass numbers also balance (222=218+4) before and after the decay.


Beta-Negative () Decay Beta particles are electrons ejected from the nucleus of an atom (not from the electron cloud that surrounds the nucleus). At first this was a bit puzzling; how can a negative electron be ejected when the nucleus contains only positive charge? Enrico Fermi had suggested in 1911 that some neutral particle in the nucleus could possibly be splitting into two other particles, one of which was the electron that was ejected. The other particle would have to be positive so that the overall charge remains the same. Eventually, once the neutron was discovered in 1932, it was realized that neutrons in the nucleus could actually split up into a proton and an electron. This means that the daughter nucleus has an atomic number 1 higher than the parent nucleus (the nucleus it turns into is the next higher element on the periodic table). Later, it was realized that another particle (called the neutrino) is also produced in this decay.

An electron can be described using the same notation used to describe a nucleus: e01 . We can

write it this way if we think of the bottom number as the electric charge on the particle since its

charge is 1 and its mass is very small (almost 0) compared to neutron or proton. An example of beta-negative decay would be the transmutation of thallium-208 into lead-208:

e01

20882

20881 Pb Tl

The atomic mass number does not change since the total number of nucleons in the nucleus remains the same (a neutron is converted to a proton). The atomic number increases by 1 since there is now 1 more proton in the nucleus.

Beta-Positive () Decay Beta-Positive decay is very similar to Beta-Negative. The main difference is that the particle that the nucleus emits is a positive version of the electron called a positron. In this case, a proton changes into a neutron, while emitting the positron. A positron is described by the notation:

e01+ .

An example of beta-positive decay would be the transmutation of magnesium-23 to sodium-23.

e01+

2311

2312 + Na Mg→

The atomic mass number does not change since the total number of nucleons in the nucleus remains the same (a proton is converted to a neutron). The atomic number decreases by 1 since there is now 1 less proton in the nucleus.


Electron Capture Although electron capture is not a decay, it is a transmutation. In this case, if a fast moving electron (from outside the atom) hits the nucleus, a proton in the nucleus can capture it and turn into a neutron. Again, the mass number will not change and the atomic number will go

down by 1. e.g. Li +B 73

01-

74 → e e

Gamma () rays Gamma rays can be emitted from the nucleus along with the alphas or betas, they do not carry away any mass or charge so the type of nucleus doesn’t change (i.e. this is not a transmutation). The symbol for a gamma ray in a nuclear

decay is 00 .

The nuclei of atoms can also exist in “excited states”, just as electrons in orbit around the nucleus can be excited to higher energy levels. If a nucleus in a higher energy level “de-excites” to a lower energy level, it can emit a gamma ray to carry away the energy it loses (it obeys the Law of Conservation of Energy).

Decay Series Often, the daughter nucleus of a radioactive decay is itself radioactive and will also decay, not necessarily in the same way as the parent. The process can be repeated several times in a decay series. This will continue until the daughter nucleus at some stage is stable. Shown are some sample decay series’ for Uranium-238 and Neptunium-237.


4) Half-Life We can't predict when any given nucleus will spontaneously decay so we can't really talk about how long it takes between decays. The decay process is a random one. But, for each type of nucleus (element) the average amount of time it takes for a nucleus to decay is constant. In a given sample of radioactive material, the more nuclei that are present, the better the chance that there will be a decay. Thus, the rate of emission depends directly on how much material there is; the more material there is, the more radioactive it will be. The number of decays that are happening each second depends on how many parent atoms are present. At the beginning, in a pure sample, the rate would be high. But as more and more decay, there are fewer atoms left and the decays become more spread out (on average). For example, in a 1 kg sample of pure U-238, 3 million nuclei will decay every second. In a decay series the time it takes for each decay step is not the same. Some steps can be very quick, some can take a long time. A useful quantity that describes how quickly a material will decay is the half-life: the amount of time it takes for one-half of the atoms of a particular radioisotope in a sample to undergo decay. The half-life is a property of the substance and doesn’t depend on how much there is in the sample, or how long it has been around. Half-lives vary widely as shown in the table. The symbol for half-life is t1/2 . Knowing the half-life of a substance allows us to predict how much will still be present in its original form as time passes. For example, assume we have a 100 g sample of a radioactive material with a half life of 12 hours. This means that after 12 hours, only 50 g of the parent material will remain. The rest will have transmuted into the daughter material. After 24 hours (two half-lives) another half of the 50 g will have decayed, so there will only be 25 g of the original substance left (and 75 g of the daughter material). After 3 half-lives (36 hours) there will now be 12.5 g left (the 25g that was present at 24 hours has reduced to ½ the amount in the next 12 hours).

Nucleus Half-Life Decay

beryllium-8 2 1016 s alpha

oxygen-10 29 s beta

iodine-131 8.04 days beta

cobalt-60 5.3 years beta

plutonium-239 24,000 years alpha

uranium-238 4.5 billion years alpha


At right is a sample decay curve showing how much of the parent nucleus is left as time passes. The x-axis is expressed in these graphs in terms of the number of half-lives that have passed. The y-axis shows the percent of the original type of nucleus that remains. This graph can be applied to any radioactive element (it is a universal decay curve) The graph at right shows the decay of Californium-252 as a function of time. We can find the half-life from the graph by looking for the time at which there is only 50% of the parent isotope left. In this graph we can see that time is about that is at about 2.7 years. We can also determine how long it will take for the rate of decay to reach a certain level. For example, imagine we have a sample of a substance that has a half-life of 50 years. If its level of radioactivity needs to reduce to 1/16th of its current level in order for it to be safe, how long will we have to wait? To answer this we need to see how many half lives would reduce the initial amount of substance to 1/16th of the original amount. Since

2

1

2

1

2

1

2

1

16

1 (1/2 multiplied by itself 4 times)

this means that we would need 4 half-lives (or 200 years) to reach the desired level. We could also use a universal decay curve to see when the percent remaining is equivalent to 1/16 (which is 6.25%). In this case the graph shows that this happens at a time of 4 half-lives.


The amount of parent material in a sample that starts out with a mass of m0 is related to time by the equation

21

02

1 //)(

ttmtm

where t (the time) is given in the same unit as the half-life.

For example, after 25 hours, for a sample of a radioisotope with an initial mass of 10 g and a half-life of 4 hours, there will only be

g 13.0013.0g 1025.6)5.0(g 10

4/25

2

1g 10)25(

m

of the original isotope remaining. The other 9.6875 g will be made of the daughter material(s). Some radioactive materials are used in medicine for radiation therapy (often for cancer). Some of these materials have very short half-lives and need to be produced locally if they are going to be used with a patient. If they have to travel too far, most of the active material will have decayed before it can be used.

Radioactive Dating The age of a sample of material can be found by looking at the amounts of radioactive materials in them. The older they are, the fewer atoms of the radioisotopes they will have (as compared to their decay products). To estimate the ages of rock formations, geologists can look at and compare the amounts of long-lived radioisotopes like uranium-235, uranium-238, rubidium-87, and calcium-40 to help establish how old a sample is. In the case of wood, bone, or other biological materials, scientists can look at the amount of carbon-14 present in a sample to find its age (carbon dating). Carbon-14 is a naturally occurring radioisotope of carbon (half-life 5730 years) and is present as a small fraction of all the carbon found in living things (most of it is carbon-12). This carbon decays, but is constantly being replenished in organisms as they consume carbon from the environment while they are alive. However, once they die, they no longer replace the carbon-14 and it begins to decay, but the carbon-12 doesn’t. By comparing the amount of carbon-14 with the amount of carbon-12 in a sample, its age can be found (or at least how long since it was no longer part of a living organism). This method works for materials less than about 60,000 years old. For samples older than that, there is too little carbon-14 to measure.

Measuring Radioactivity To describe the level of radioactivity, two units that are commonly used are the bequerel (Bq) and the curie (Ci). These each describe a certain number of emissions or decays in each second:

1 Bq = 1 decay/second 1 Ci = 3.7×107 decay/second

These units include all forms of radiation, so they don’t necessarily tell us how dangerous the source is.


Another unit is the Radiation Absorbed Dose, or rad. This is a measure of how much energy has been absorbed in the form of radiation. 1 rad means that 1 gram of tissue will have absorbed 1/100,000th of a Joule of energy. The Gray (Gy) is a similar type of unit where 1 Gy = 100 rad. The rad describes the energy absorbed from all types of radiation, but some types are more dangerous than others. To reflect this, there is another unit called the rem (Roentgen Equivalent Man). The higher the rem value, the more dangerous a radiation dose is. Typical average absorbed doses of radiation from natural and environmental sources are around 300 mrem (millirems) in a year. A typical chest x-ray might give a dose of about 10 mrem. A related unit used in the SI system is the Sievert (Sv) where 1 Sv = 100 rem. In this unit, the average annual dose would be about 3 mSv. The chart below shows some typical doses and the maximum allowable radiation dose from different sources. The actual measurement of radioactivity is often done using Geiger counters which detect the radiation using a Geiger-Muller tube. These tubes contain a gas and have a high voltage applied to them. Normally the gas is not a conductor, but if radiation passes through the gas, it can knock electrons free from the gas molecules and the electrons are free to move around. Since there is a voltage applied to the tube, every time electrons are freed, the gas briefly conducts electricity. This brief burst of electric current is used to indicate that radiation has been detected, either by deflecting a needle or making a sound (usually a “click”) or changing a counter.


5) Nuclear Reactions Many elements undergo transmutation naturally (radioactive decay) but transmutation can also be artificially induced (caused) by bombarding nuclei with other particles. When transmutation is caused this way it is called a nuclear reaction. The products of a nuclear reaction are not necessarily alpha, beta, or gamma emissions. They depend on the nucleus we begin with and what it is bombarded with.

Many of these reactions involve protons and neutrons and we need symbols to describe these particles. A proton contains one nucleon and it has one positive charge. A neutron has a charge of 0 and it contains one nucleon. Their symbols are shown at right.

Rutherford was the first person to observe nuclear reactions when he aimed alpha particles (from a radioactive source) at a tube full of nitrogen gas (in 1919). Afterward he found that there was some oxygen in the tube, and he detected protons leaving the tube. He realized that this was the result of an interaction between the alpha particles (helium nuclei) and the nitrogen nuclei.

p11

178

42

147 O He N

The nitrogen was transmuted to oxygen: this is NOT a chemical reaction (in chemical reactions, the types of atoms never change). Rutherford noticed that energy was also produced in the form of kinetic energy of the protons.

In 1932 Cockcroft and Walton were able to use protons (hydrogen) as the bombarding particles with lithium-7 to produce two alpha particles (after producing a highly unstable beryllium-8).

He He Be Li 42

42

84

11

73 p

One difficulty with using alpha particles or protons to start the transmutation is that it is hard to get them into the nucleus. This is because they both have a positive charge and so does the nucleus. As a result, the nucleus strongly repels the alpha or proton. To overcome this, they have to be moving very fast.

Neutrons can also be used to bombard nuclei to initiate transmutation. One advantage is that they don’t need to be moving very fast since they are electrically neutral. They are particularly important in the reactions that power nuclear reactors.

e.g. H He Li 31

42

10

63 n

The neutrons themselves can be produced by a nuclear reaction where alpha particles are aimed at beryllium target. This turns the beryllium into carbon and releases some neutrons (which can then strike other targets). This was what led Chadwick to the discovery of the neutron in 1932.

n10

126

42

94 C He Be

There are two basic types of nuclear reaction which are characterized by whether the products are smaller than the parent nucleus (fission) or bigger than the parents (fusion).

proton: p11

neutron: n10


Nuclear Fission

In the early experiments that used protons and alpha particles to bombard nuclei, the immediate product of the reaction was larger than the parent nucleus (they had essentially stuck together). However, in 1938, Enrico Fermi was using neutrons to bombard a sample of uranium in the hopes of building a larger nucleus. He was surprised to find that in fact the products of the reaction were smaller nuclei, about half the size of the uranium. This was the first example of an induced nuclear fission reaction. In nuclear fission a heavy parent nucleus is triggered to split up into two smaller nuclei as well as possibly neutrons and energy (in the form of electromagnetic radiation and kinetic energy of the neutrons).

e.g. nn 10

9236

14156

10

23592 3 Kr Ba U

The same type of nucleus can split up into several different pairs of products (e.g. U-235 can also split into strontium and xenon).

Notice that the atomic numbers balance on both sides; 92 + 0 = 56 + 36 + (3×0) as do the mass numbers; 235 + 1 = 141 + 92 + (3×1). Also note that the 0 and 1 of the neutron are multiplied by 3 since there are 3 neutrons.

Very large, unstable nuclei can also experience spontaneous fission in which case, they do not need to be hit by other particles. For example, U-235 can decay into Xe-140 and Sr-95.

Sr Xe U 9538

14054

23592

Nuclear Fusion

When small nuclei collide, they can stick together to form larger nuclei. This is called nuclear fusion. In order for this to happen, as mentioned before, the particles have to be moving very fast (to overcome their electric repulsion). The products of this type of reaction can also be neutrons as well as a lot of energy in the form of electromagnetic radiation and kinetic energy of the particles. An example would be the fusion of two deuterium particles (hydrogen-2) to make helium-3 and a neutron:

n10

32

21

21 He H H

These reactions can also involve other particles. For example, reactions in the Sun turn ordinary hydrogen into helium with the help of electrons:

He 2 H 4 42

01

11 e

(this simple equation actually represents a series of more complex reactions, but the end result is that 4 hydrogen nuclei and 2 electrons produce 1 helium nucleus). In this case, the total

atomic number before the reaction is (4×1) + (2×(1)) = 2, which is the same as the atomic number after the reaction. The same applies to the mass number.


proton = 1.6726×1027 kg

neutron = 1.6749×1027 kg

helium nucleus = 6.6447×1027 kg

Energy in Nuclear Reactions

Nuclear reactions produce a lot of energy in the form of electromagnetic radiation as well as kinetic energy in the particles that are produced. For a while, it was a puzzle as to where this energy came from (the Law of Conservation of Energy says it can just appear from nowhere). However, it was eventually realized that when you added up the masses of the particles that went into the reactions, it is not the same as the total mass after the reaction. In fact, the total mass after the reaction was less than the total mass before (this is different from a chemical reaction; in a chemical reaction the mass afterward is always the same as the mass before). It is the missing mass (also called the mass-deficit) that is responsible for the energy.

In 1905, Albert Einstein had shown as a result of his Special Theory of Relativity that the mass of matter particles should be considered as a form of energy. He found that the “mass-energy” of a particle or object with mass m is given by

2mcE where c is the speed of light (3.00×108 m/s).

This means that mass can be converted into other forms of energy (and the reverse is also true). For example, if 1.0 kg of water was completely converted to energy, it would produce

J1009m/s) 10(3.00kg 01 16282 ..mcE

of energy! In the process, the particles that make up the water would disappear completely and the energy would appear as electromagnetic radiation.

In the case of nuclear reactions, the small amount of mass that seems to disappear is converted into the energy produced by the reaction. For example, in the reaction

nn 10

9236

14156

10

23592 3 Kr Ba U

the products have a mass that is 0.311×1027 kg less than that of the original uranium and neutron. This means that one of these reactions produces

J10802m/s) 10(3.00kg100.311 1128272 .mcE of energy.

This is not a lot, but if there are many reactions, a large amount of energy can be produced. As another example, consider what would happen if two protons (hydrogen nuclei) could fuse with two neutrons to produce an helium nucleus.

He 2 H 2 42

10

11 n

The masses of these particles are given at right.

The total mass before is then

kg 106950.6106749.12106726.12 272727T

m .

The mass after the reaction is the mass of the helium nucleus, so the “lost” mass is

kg 1005030kg 1064476kg 1069506 272727 ... and the energy produced by the

reaction is

J10534m/s) 10(3.00kg100.0503 1228272 .mcE .


Chain Reactions

The energy in any one reaction is extremely small, but if we could cause many reactions, a lot of energy could be produced. In the case of uranium fission, at first it would seem that we would need to keep bombarding it with neutrons to trigger the reactions. But, if we look at the products of the reaction, 3 neutrons are produced. If these neutrons manage to hit uranium nuclei, they can trigger 3 more reactions, which will each release 3 new neutrons (for a total of 9). These 9 neutrons might also be able to trigger even more reactions. In this way we can get a runaway series of reactions where just one initial reaction can trigger many following reactions, each of which produces more energy. This is called a chain reaction (see diagram). For the chain to continue, it is important that the free neutrons actually hit a nucleus before leaving the material. This means that the sample of fissionable material has to be fairly pure. Otherwise the neutrons may end up being absorbed by materials that don’t react, or exit the material without encountering another uranium nucleus. If the material is pure, the reactions will proceed extremely quickly and release a large amount of energy in a very small time (an uncontrolled explosion). The rate of reaction can be controlled by the presence of other materials that will absorb neutrons (as in nuclear reactors). Surprisingly, if the neutrons that are produced are moving too fast, they might not be able to be absorbed by other nuclei to keep the chain going. To help slow down the neutrons, a substance known as a moderator is used (heavy water is one example).

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