Fundamental Nuclear Physics PDF

Nuclear Physics Chapter Contents The Nucleus Radioactivity Applications of Nuclear Physics Fundamental Forces and Elementary Particles  As you will recall, the nucleus is the region of space at the center of the atom that contains all the atom's positive charge and almost all its mass....

Nuclear Physics Chapter Contents The Nucleus Radioactivity Applications of Nuclear Physics Fundamental Forces and Elementary Particles  As you will recall, the nucleus is the region of space at the center of the atom that contains all the atom's positive charge and almost all its mass. The simplest nucleus is that of the hydrogen atom. The nucleus consists of a single proton, with an electric charge +e. All other nuclei contain neutrons in addition to protons. The neutron is an electrically neutral particle (its electric charge is zero) with a mass just slightly greater than that of the proton.  Collectively, protons and neutrons are known as nucleons. Nuclear physics is the study of how nucleons interact with one another in a nucleus. The following figure shows how nucleons are represented.  A good way to think of a nucleus is like a bag of marbles, with the closely packed marbles similar to the nucleons. This close packing in an incredibly small space results in an enormous density of approximately 2.3 x 1017 kg/m3. A typical nucleus, like the one illustrated in the figure on the next slide, is described in terms of the numbers and types of nucleons it contains.  The atomic number, Z, is defined as the number of protons in a nucleus. The number of neutrons in a nucleus is designated by the neutron number, N. Finally, the total number of nucleons in a nucleus is the mass number, A.  Thus, the mass number is the sum of the atomic number and the neutron number: A=Z+N The composition of a nucleus is expressed with special notation. In general, the nucleus of an element X, with atomic number Z and mass number A is written as follows: A ZX For example, the nucleus of carbon-14 is written as follows:  Notice that the letter C is the chemical symbol for carbon. The atomic number, Z = 6, is written as a subscript in front of the chemical symbol. Likewise, the mass number, A = 14, is written as a superscript. A similar type of notation is used for subatomic particles—such as the nucleons. Neutrons and protons are represented as follows: = neutron (mass number 1, charge 0) = proton (mass number 1, charge 1) When nuclei contain a large number of neutrons and protons, a circle representing the nucleus is drawn. Inside the circle we write the symbols for neutrons and protons, along with the number of each type of particle. An example is shown in the figure below. The following example shows how to write a symbol representing a nucleus. Because different isotopes have different numbers of neutrons, they also have different masses. Masses are given in atomic mass units. The atomic mass unit (u) is a unit of mass exactly equal to 1/12 the mass of a carbon-12 atom. In other words, the mass of one atom of. is exactly 12 u. The value of the atomic mass unit in kilograms is as follows:  All nuclei of a given element have the same number of protons. However, atoms of a given element can have different numbers of neutrons in their nuclei. Nuclei with the same number of protons (the same value of Z) but different numbers of neutrons (different values of N) are referred to as isotopes. For example, and.. are two isotopes of carbon, with.6 being the most common one, constituting 89.89% of naturally occurring carbon. The following table gives the mass and charge of particles in the atom. One of Albert Einstein's most famous results is the relationship between mass and energy. According to Einstein, mass and energy are equivalent, with energy equal to mass times the speed of light squared. This equation for mass-energy equivalence is as follows: As an example, let's apply the mass-energy equivalence to a mass equal to the atomic mass unit, 1 u.  Substituting 1.660539 x 10−27 kg (the mass of 1 u in kilograms) for m yields E = mc2 = (1.660539 x 10−27 kg)(2.998 x 108 m/s2)2 = 1.492 x 10−10 J Converting to electron volts gives E = (1.492 x 10−10 J)(1 eV/1.6022 x 10−19 J) = 9.315 x 108 eV This is a significant amount of energy compared to the 13.6 eV required to ionize a hydrogen atom. ‫الكترون فولت هو وحدة قياس طاقه الحركه التي يكتسبها الكترون واحد غير‬ ‫مرتبط عند تسريعه بواسطة جهد كهربائي ساكن قيمته ‪ 1‬فولت في الفراغ‪.‬‬ ‫وطبقا لهذا التعريف باأللكترون فولت حاصل ضرب ‪ 1‬فولت في شحنة األلكترون‬ ‫(كولوم ‪1.6023x10-19‬التي تقدر ب )أي أن‬ ‫‪1 ev = 1.6023 x10 -19 volt.colum‬‬ ‫بما ان ‪ 1‬فولت = ‪ 1‬جول ‪ /‬شحنة االلكترون بالكولوم نحصل علي العالقه بين األلكترون‬ ‫فولت والجول وهي‬ ‫‪1eV =1.6023 x 10-19 Joule‬‬ ‫وحدة الجول كبيره جدا بالنسبه لتطبيقها علي األلكترونات لهذا اخترع الفيزيائيون وحدة للطاقه‬ ‫الصغيره لتسهيل الحسابات عند دؤاسة الذره والجسيمات األوليه وهي وحدة االلكترون فولت‬ ‫‪ 1‬جول =‪ 1‬كيلوجرام‪.‬متر‪ /2‬ثانيه‪2‬‬  As a general rule, atomic energies are in the range of electron volts (eV), whereas nuclear energies are in the range of millions of electron volts (MeV), where 1 MeV = 106 eV. We conclude, then, that 1 atomic mass unit, or 1 u, is equivalent to an amount of energy, Eu, where Eu = 931.5 MeV This conversion between mass and energy will be used later in the study of nuclear reactions. It should be noted that all the energy in the universe is the result of mass being converted to energy.  Thus, if protons in a nucleus experienced only the electrostatic force, the nucleus would fly apart. Because this does not happen, it follows that large attractive forces also act within the nucleus. The attractive force that holds a nucleus together is called the strong nuclear force. The properties of the strong nuclear force are as follows: The strong nuclear force acts over a very short range (~10−15 m). The strong nuclear force is always attractive. The strong nuclear force does not act on electrons.  The competition between the repulsive electrostatic forces and the attractive strong nuclear force determines whether a given nucleus is stable. The following figure shows the neutron number, N, and the atomic number, Z, for stable nuclei.  Small nuclei—those with relatively small atomic numbers—are most stable when they have nearly equal numbers of neutrons (N) and protons (Z). For example,.. and.. are both stable. The condition N = Z is indicated by the straight line in the previous figure. As the atomic number increases, stable nuclei deviate from the line N = Z. In fact, large stable nuclei tend to contain significantly more neutrons than protons. An example is , which has 110 neutrons but only 75 protons.  Radioactivity In fact, the largest number of protons in a stable nucleus is Z = 83, corresponding to the element bismuth. Nuclei with more than 83 protons are simply not stable. Large, unstable nuclei can decay in a number of ways. When an unstable nucleus decays, it emits particles of high-energy photons. The particles and photons emitted when a nucleus decays are known as radioactivity.  Four types of radioactivity decay are most common. Three involve the emission of particles, and one involves the emission of an energetic photon. Alpha particles (denoted by the Greek letter α) consist of two protons and two neutrons. They are actually the nuclei of helium atoms,.. When a nucleus decays by giving off alpha particles, we say that it emits α rays. Beta particles (denoted by the Greek letter β) are electrons that have been given off during radioactive decay. When a nucleus gives off an electron, we say that it emits a β− ray.  A positron, short for "positive electron," is the antiparticle to an electron. Positrons have the same mass as an electron, but the opposite charge (+e). If a nucleus gives off positrons when it decays, we say that it emits β+ rays. In a nuclear equation, we write a positron as e+. A nucleus in an excited state can drop to a lower- energy state and emit a high-energy photon known as a gamma ray. We denote gamma rays with the Greek letter γ.  Radioactivity was discovered by the French physicist Antoine Henri Becquerel (1852–1908). He observed that uranium was able to expose photographic film, even when the film was covered. This was proof of the penetrating ability of radioactivity. Typical penetrating abilities for three types of rays are as follows: Alpha (α) rays can barely penetrate a sheet of paper and are stopped by a sheet of aluminum. Beta rays (both β− and β+) can penetrate a few millimeters of aluminum.  Gamma (γ) rays pass right through a thin aluminum sheet and can even penetrate several centimeters of lead. When a large nucleus (larger than iron) undergoes radioactive decay, the mass of the system decreases. The figure on the next slide shows that the mass of a large nucleus before decay is greater than the mass of the resulting nucleus plus the mass of the particles it emits. A similar change in mass occurs with small nuclei. For example, the mass of a helium nucleus is less than the mass of 2 protons and 2 neutrons that are separated from one another, as is indicated in the figure below.  This means that energy will be released if 2 protons and 2 neutrons are put together to form a helium nucleus. In general, the difference in energy between a complete nucleus and its separated individual parts is referred to as the nuclear binding energy. Nuclear binding energy is released when small nuclei are fused together to form a larger nucleus, in a process called fusion, and also when large nuclei decay into smaller nuclei, in a process called fission. The energy released in fusion or fission corresponds to a decrease in mass, according to E = |Δm|c2.  When a nucleus decays by giving off an α particle, it loses two protons and two neutrons. As a result, its atomic number, Z, decreases by 2, and its mass number, A, decreases by 4. Symbolically, this process can be written as follows: In this decay, X is referred to as the parent nucleus, and Y is the daughter nucleus. The sum of the atomic numbers on the right side of the reaction is equal to the atomic number on the left side. The same is true for the mass numbers.  The following example illustrates how the energy released when a nucleus undergoes alpha decay is determined.  The basic process that occurs in beta decay is the conversion of a neutron to a proton, an electron (e−), and an antineutrino. neutron proton + electron + antineutrino Neutrinos have very little mass (about a hundred- thousandth of the mass of an electron) and little interaction with matter. Only 1 in every 200 million neutrinos that pass through the Earth interacts with it in any way.  The force responsible for beta decay is known as the weak nuclear force. This force is short range and is important only within the nucleus of an atom. When a nucleus decays by giving off an electron, its mass number is unchanged (since protons and neutrons count equally in determining A), but its atomic number increases by 1. The process can be represented symbolically as follows:  In some cases a nucleus gives off a positron (e+) rather than an electron. In the following example, the energy released when carbon-14 undergoes beta decay is determined.  An atom in an excited state can emit a photon when one of its electrons drops to a lower energy level. Similarly, a nucleus in an excited state can emit a photon as it decays to state of lower energy. High-energy photons emitted by nuclei are known as gamma (γ) rays. Consider the following decay process: The asterisk on the nitrogen symbol indicates that the nitrogen nucleus has been left in an excited state as a result of beta decay.  Subsequently, the nitrogen nucleus may decay to its ground state, with the emission of a γ ray. Radioactive decays may occur in series. Consider an unstable nucleus that decays and produces a daughter nucleus. If the daughter nucleus is also unstable, it eventually decays and produces its own daughter nucleus, which may in turn be unstable. In such cases, an original parent nucleus can produce a series of related nuclei in a process referred to as a radioactive decay series.  An example of a radioactive decay series is shown in the figure below. As the figure indicates, as uranium-235 decays, it changes to a number of intermediate nuclei Before becoming the stable nucleus at the end of the series, lead-207.  Notice that several of the intermediate nuclei in this series can decay in two different ways—either by alpha decay or by beta decay. The rate at which nuclear decay occurs—that is, the number of decays per second—is referred to as the activity. A highly active material has many nuclear decays occurring in one second. For example, a typical sample of radium (usually a fraction of a gram) might have 105 to 1010 radioactive decays per second.  The unit used to measure activity is the curie, named in honor of Pierre Curie (1859–1906) and Marie Curie (1867–1934), pioneers in the study of radioactivity. The curie (Ci) is defined as follows: 1 curie = 1 Ci = 3.7 x 1010 decays/s The reason for this choice is that 1 Ci is roughly the activity of 1 g of radium. In SI units, activity is measured in terms of the becquerel (Bq): 1 becquerel = 1 Bq = 1 decay/s  Applications of Nuclear Physics Chemical reactions involve changes to the electron clouds that surround a nucleus; nuclear reactions involve changes to neutrons and protons within the nucleus. Nuclear reactions generally have no effect on chemical reactions, and chemical reactions don't alter the behavior of the nucleus. Just as chemical reactions are an important part of our everyday lives, so too are nuclear reactions.