Quanta to Quarks Focus Area 3
The Nucleus • Typically the nucleus is less than one ten-thousandth the size of the atom, the nucleus contains more that 99.9% of the mass of the atom. • Nuclei consist of positively charged protons and electrically neutral neutrons held together by the so called strong nuclear force. • This force is much stronger than the repulsive electrostatic (Coulomb) force, but its range is limited to distances on the order of a few (10-15) metres.
The number of protons in the nucleus, Z, is called the atomic number. This determines what chemical element the atom is. • The letter N denotes the number of neutrons in the nucleus. The atomic mass of the nucleus, A = Z + N • and gives the total number of nuclear particles in the nucleus which are collectively referred to as nucleons. • Protons carry a charge of 1.602 × 10-19C. Neutrons carry no charge. Protons have a mass of 1.672 × 10-27 kg. Neutrons are slightly more massive with a mass of 1.675 × 10-27 kg.
Wait…when did they find the neutron? • As early as 1907 it had been suggested that protons alone were not sufficient to account for the mass of most atoms. • It was suspected that there must be another nucleon, with considerable mass, but no electric charge. • The existence of the neutron was proven in 1932 by James Chadwick (1891-1974). • It was impossible then to detect and measure neutrons directly. • The method Chadwick used relied upon neutrons colliding with other particles, then applying the scientific principles of Conservation of Energy and Conservation of Momentum to measure the properties of the neutron.
In 1920, Rutherford guessed that there had to be a new kind of particle in the nucleus, about as heavy as a proton but with no electric charge, which he called the neutron. • Others thought that whatever it was in the nucleus might be high energy gamma ray photons (radiation had been discovered by then). • In 1932, Frederic & Irene Joliot (Irene was the daughter of Marie Curie) fired alpha particles (helium nuclei) at beryllium and it was seen that the beryllium ejected something from the nucleus that caused paraffin to release protons. • Whatever it was could pass through thick sheets of lead, but they were stopped by water or paraffin wax.
Since large numbers of very energetic protons were emitted from the paraffin when it absorbed whatever was coming out of the nucleus, they assumed that whatever was being ejected from the beryllium nuclei must be an extremely energetic form of gamma radiation. Chadwick, however, disagreed. • Chadwick showed that whatever was ejected from the beryllium nuclei could not be radiation because it did not have sufficient energy to then eject protons from paraffin wax. Whatever it was that could knock protons out of other atoms had to be a fairly heavy particle, not a massless particle such as gamma radiation. • Another result that suggested that the unknown radiation was not gamma rays is that they did not discharge a charged electroscope, whereas gamma rays do discharge a charged electroscope due to the photoelectric effect.
Using the velocity of the ejected protons and the laws of conservation of energy and momentum, Chadwick calculated the mass of the unknown particle. It was just a little heavier than the proton. He had no doubt that this was Rutherford's neutron. • Chadwick explained the process occurring in the experiment as: • Chadwick explained that when the neutrons emitted from the beryllium collided with the light hydrogen nuclei in the paraffin, the neutron came to a sudden stop and the hydrogen nucleus (proton) moved off with the same momentum as the neutron had before the collision.
Radioactivity • Henri Becquerel discovered radioactivity in 1896. • Ernest Rutherford studied this new phenomenon and found that there were two different types of radiation that could be emitted from radioactive elements. • To distinguish between them he called them alpha and beta radiation. • When Paul Villard found a third type of radiation in 1900, Rutherford called it gamma radiation.
Transmutation • Rutherford and Frederick Soddy discovered that atoms change from one element to another as a result of emitting radiation. • This is called transmutation. • Transmutation is a nuclear reaction where the structure of the nucleus changes, emitting particles or a gamma ray in the process. • Rutherford received the Nobel Prize in Chemistry in 1908 for this work.
Alpha Decay • Alpha decay occurs in atoms which have a very large nucleus and are unstable. To achieve greater stability, the nucleus may spontaneously eject an alpha particle to carry away excess mass and energy.
Beta Decay • Some atomic nuclei, of any size, have an unstable mix of protons and neutrons. If there is an excess of neutrons, a neutron can be turned into a proton plus an electron. • The result is that: Number of neutrons decreases by 1, Number of protons increases by 1. (This means Atomic Number goes up by 1 but Atomic Mass Number does not change), The electron is ejected from the nucleus at high speed. This is the Beta particle... a high speed electron.
When a nucleus ejects a positron ( ) as a result of beta decay, its atomic number will decrease by 1 but its mass number will remain unchanged. In this case, a neutrino (ν) will also be ejected. A neutrino also has no charge and little mass. • This is called beta plus (β+) decay. The positron is produced when a proton changes into a neutron. The positron carries away the excess charge, as shown below. • The general equation for β+ decay is shown below:
Line of Stability • Nuclides that are above the line of stability tend to move closer to it by releasing an α particle. • Nuclides that are to the left of the line of stability (i.e. contain too many neutrons) tend to move toward stability using β- decay. • Nuclides that are to the right of the line of stability tend to undergo β+ decay in order to become more stable.
Gamma Radiation • Gamma (γ) rays are high frequency electromagnetic waves that carry away excess energy from unstable nuclei. The unstable nuclei are shown by the letter ‘m’ (for metastable) after the mass number, or by an asterisk after the element symbol. • The parent nucleus is usually unstable because it was formed as a result of α or β decay. Therefore, γ decay usually follows α or β decay. This may happen immediately, or some time later.
Jimmy Neutrino • The neutrino was first postulated in 1930 by Wolfgang Pauli to preserve the laws conservation of energy and momentum in beta decay. • He theorized that an undetected particle was carrying away the observed difference between the energy and momentum of the initial and final particles in beta decay.
Pauli originally named his proposed light particle a neutron. • When James Chadwick discovered a much more massive nuclear particle in 1932 and also named it a neutron, this left the two particles with the same name. • Enrico Fermi, who developed the theory of beta decay, coined the term neutrino in 1934 as a way to resolve the confusion. • It is the Italian equivalent of "little neutral one".
During decay it was found that beta particles could have a range of kinetic energies rather than one specific energy as in alpha decay. • It was proposed that the total energy lost by the nucleus during decay was shared by the neutrino and the electron being ejected. • Since the kinetic energy of the electron varied, there must be another particle whose kinetic energy could also vary so that the sum of their energies was always the same. The simultaneous emission of a beta particle and a neutrino in beta decay allowed for energy and momentum to be conserved. This theory was accepted for almost a quarter of a century without any direct evidence to support it. In 1956, an experiment was performed in a nuclear reactor that could only occur if the neutrino actually existed, thus confirming its existence.
Fermi’s Firm Findings • After the discovery of the neutron which was large and uncharged, Enrico Fermi tried to extend the number of known elements through transmutation. • In 1934 he bombarded uranium-235 with neutrons expecting that the uranium would take up the neutron and then it would undergo beta decay to produce an isotope of neptunium as shown in the equation below. • Two lighter nuclei were actually produced as fission products in an artificial transmutation as shown in the equation below. • Fermi has actually succeeded in producing the first artificial transmutation using nuclear fission - when heavier nuclei are split into two or more lighter nuclei.
Large nuclei are unstable because protons at the surface of the nucleus are repelled by a force proportional to the total number of protons in the nucleus, but attracted towards the interior by a force proportional to the number of nucleons in its immediate vicinity (which is constant for light or heavy nuclei). • Thus the electrical repulsion sets a maximum limit to the number of protons in a nucleus. • The maximum limit to the number of neutrons is set by the strong nuclear force that seeks to bind pairs of neutrons to pairs of protons. • Thus if the neutron excess becomes too large, a neutron spontaneously changes into a proton. • Since very heavy nuclei have too many of both neutrons and protons, they spontaneously emit tightly bound nuclear sub assemblies. This is naturally occurring fission or transmutation.
Fission or transmutation may be artificially triggered by bombardment with neutrons. • Heavy nuclei break up under such bombardment into a pair of lighter nuclei with the release of energy far exceeding the total kinetic energy of the colliding particles. This excess energy is due to the reduction of nuclear mass. As stated, some nuclei can be made unstable by firing an extra neutron into them. This is called a fission reaction because the nuclei split into two fragments. When the nucleus decays, more neutrons are ejected. If these neutrons cause further fissions to occur a chain reaction occurs. At each step of this process, mass is converted into energy which is released as the kinetic energy of the particles in the system. Controlled chain reactions produce enormous amounts of energy this way and they take place in nuclear reactors, which use a fissionable material such as uranium-235.
Forces • What holds the nucleus together? • This question had been asked as soon as Rutherford had proposed that atoms have a nucleus. There were just 2 forces then understood, which could be operating in the nucleus. • Gravity: All masses attract all other masses by gravity. This would attract all nucleons to each other. • Electrostatic Forces:All charged particles exert a force on other charged particles. This force would not act on neutrons, but should cause protons to be repelled by other protons. • Calculations showed that the electrostatic repulsion would be much, much stronger than gravity. The nucleus should instantly fly apart!
Someone has a STRONG feeling about this • Since the nucleus does exist, and doesn’t instantly explode, it was realized that there must be another force operating. • It was called simply the “Strong Nuclear Force”. Its properties could be inferred and calculated: • It must be much stronger than the proton proton electrostatic repulsion. (it’s over 100X stronger) • It must be independent of charge and attract all nucleons... protons & neutrons. • It must be extremely short-ranged, operating only across the tiny distances of the nucleus. (Otherwise it might cause neighbouringatomic nuclei to fuse together, and eventually pull all matter into one lump!)
The “atomic mass unit” (u) is a measure of mass devised for convenience in Chemistry. Roughly speaking, both a proton and a neutron have a mass of 1 u, although in the calculations following, you need to be much more precise. • Obviously, 1 u is a very small mass: 1 u = 1.661x10-27 kg • You need to be able carry out calculations using either unit, so the following data may be useful.
The “electron-volt” (eV) is an energy unit that is convenient because the energy of sub-atomic particles has traditionally been measured by their behaviourwithin electric fields. 1 eV is the energy gained by an electron accelerating in an electric field with a potential difference of 1 volt. 1 eV is an extremely small amount of energy: 1 eV = 1.602 x 10-19 joules of energy • so the unit often used is the mega-electron-volt (MeV) 1 MeV = 1x106 (one million) eV • This is convenient when dealing with individual atoms or particles.
There is something defective here • It was realized that incredibly powerful forces were operating within the atomic nucleus. How could such forces arise? • The answer lies in the fact that the mass of every atomic nucleus (except hydrogen ) DOES NOT ADD UP. • An alpha particle or helium nucleus has a mass of 4.00150 u. If we were to add the masses of two protons and two neutrons we would get a mass of 4.03190 u for an alpha particle. • The sum of the inidividual masses of the protons and neutrons is 0.03040 u larger than the sum of the alpha particle as a whole. • This difference in mass is known as the mass defect and it represents the mass lost when a nucleus is assembled from its constituent parts. • As you would expect, the mass lost in assembling the nucleus is converted to energy and this energy is used to bind the nucleus together.
In a bind • We could convert the mass from atomic mass units to kilograms and then use ΔE=Δmc2 to calculate the energy used to bind the nucleus together in joules. • But these numbers are not convenient so instead we calculate the energy in electronvolts using the mass in atomic mass units. Since 1 u is equivalent to 931.5 MeV/c2 we can calculate the binding energy as follows: ΔE = Δmc2 = 0.03040 x 931.5 = 28.3 MeV • The binding energy of a particular nucleus will depend the total number of nucleons in the nucleus so large nuclei will have higher binding energies. • To make standardised comparisons between light and heavy nuclei we use a standard called the binding energy per nucleon. For the helium nucleus above the binding energy per nucelon would be 28.3 / 4 = 7.075 MeV.
Fermi’s Demo • Fermi achieved the first artificially produced nuclear fission in 1934. He was able to irradiate unranium-235 with slow neutrons and produce a radioactive product that produced alpha particles. • He incorrectly assumed that this product was an isotope of neptunium (atomic number 93) but later the products were discovered to be the lighter elements of bromine and lanthanum.
Fermi in 1939, escaped to the United States where he continued his research into fission. Delayed by economic and security constraints, he secretly build Chicago Pile 1, the world’s first nuclear fission reactor in 1942. • Having theoretically calculated that fission was possible from naturally occurring uranium, he set about construction of a pile of graphite blocks to slow or moderate the speed at which the neutrons would travel. • He used cadmium control rods to absorb neutrons and control the rate of reaction. This demonstration of a controlled nuclear fission reaction started an accelerated program by the US army to develop a nuclear bomb, the Manhattan Project.
Controlled & Uncontrolled Nuclear Reaction Chains • Homework: • Compare Controlled & Uncontrolled Nuclear Reaction Chains. • Due: On Edutone by tomorrow
Wilson Cloud Chamber • http://youtu.be/NeydrHKvpYM