2.3 Atomic Mass and Number
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Neutron Stars
Chandra X-Ray Observatory X-Ray Astronomy Field Guide Neutron Stars Ordinary matter, or the stuff we and everything around us is made of, consists largely of empty space. Even a rock is mostly empty space. This is because matter is made of atoms. An atom is a cloud of electrons orbiting around a nucleus composed of protons and neutrons. The nucleus contains more than 99.9 percent of the mass of an atom, yet it has a diameter of only 1/100,000 that of the electron cloud. The electrons themselves take up little space, but the pattern of their orbit defines the size of the atom, which is therefore 99.9999999999999% Chandra Image of Vela Pulsar open space! (NASA/PSU/G.Pavlov et al. What we perceive as painfully solid when we bump against a rock is really a hurly-burly of electrons moving through empty space so fast that we can't see—or feel—the emptiness. What would matter look like if it weren't empty, if we could crush the electron cloud down to the size of the nucleus? Suppose we could generate a force strong enough to crush all the emptiness out of a rock roughly the size of a football stadium. The rock would be squeezed down to the size of a grain of sand and would still weigh 4 million tons! Such extreme forces occur in nature when the central part of a massive star collapses to form a neutron star. The atoms are crushed completely, and the electrons are jammed inside the protons to form a star composed almost entirely of neutrons. -
Applications of the Variational Monte Carlo Method to the Ground States of the Lithium Atom and Its Ions up to Z = 10 in the Presence of Magnetic Field
Applications of the Variational Monte Carlo Method to the Ground States of the Lithium Atom and its Ions up to Z = 10 in the Presence of Magnetic Field S. B. Doma1), M. O. Shaker2), A. M. Farag2) and F. N. El-Gammal3) 1)Mathematics Department, Faculty of Science, Alexandria University, Egypt E-mail address: [email protected] 2) Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt 3)Mathematics Department, Faculty of Science, Menofia University, Shebin El-Kom, Egypt Abstract The variational Monte Carlo method is applied to investigate the ground state energy of the lithium atom and its ions up to = 10 in the presence of an external magnetic field regime with = 0 ~ 100 a.u. Our calculations are based on using three forms of compact and accurate trial wave functions, which were put forward in calculating energies in the absence of magnetic field. The obtained results are in good agreement with the most recent accurate values and also with the exact values. Key Words: Atoms in external magnetic field, Variational Monte Carlo method, Lithium atom, Lithium like ions, Total energy. Introduction Over the last decade continuing effort has gone into calculating, with ever increasing accuracy and with various methods, the energies of atoms and ions in neutron star magnetic fields. The motivation comes largely from the fact that features discovered [1–3] in the thermal emission spectra of isolated neutron stars may be due to absorption of photons by heavy atoms in the hot, thin atmospheres of these strongly magnetized cosmic objects [4]. Also, features of heavier elements may be present in the spectra of magnetic white dwarf stars [5, 6]. -
An Introduction to Isotopic Calculations John M
An Introduction to Isotopic Calculations John M. Hayes ([email protected]) Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA, 30 September 2004 Abstract. These notes provide an introduction to: termed isotope effects. As a result of such effects, the • Methods for the expression of isotopic abundances, natural abundances of the stable isotopes of practically • Isotopic mass balances, and all elements involved in low-temperature geochemical • Isotope effects and their consequences in open and (< 200°C) and biological processes are not precisely con- closed systems. stant. Taking carbon as an example, the range of interest is roughly 0.00998 ≤ 13F ≤ 0.01121. Within that range, Notation. Absolute abundances of isotopes are com- differences as small as 0.00001 can provide information monly reported in terms of atom percent. For example, about the source of the carbon and about processes in 13 13 12 13 atom percent C = [ C/( C + C)]100 (1) which the carbon has participated. A closely related term is the fractional abundance The delta notation. Because the interesting isotopic 13 13 fractional abundance of C ≡ F differences between natural samples usually occur at and 13F = 13C/(12C + 13C) (2) beyond the third significant figure of the isotope ratio, it has become conventional to express isotopic abundances These variables deserve attention because they provide using a differential notation. To provide a concrete the only basis for perfectly accurate mass balances. example, it is far easier to say – and to remember – that Isotope ratios are also measures of the absolute abun- the isotope ratios of samples A and B differ by one part dance of isotopes; they are usually arranged so that the per thousand than to say that sample A has 0.3663 %15N more abundant isotope appears in the denominator and sample B has 0.3659 %15N. -
Mass Spectrometry: Quadrupole Mass Filter
Advanced Lab, Jan. 2008 Mass Spectrometry: Quadrupole Mass Filter The mass spectrometer is essentially an instrument which can be used to measure the mass, or more correctly the mass/charge ratio, of ionized atoms or other electrically charged particles. Mass spectrometers are now used in physics, geology, chemistry, biology and medicine to determine compositions, to measure isotopic ratios, for detecting leaks in vacuum systems, and in homeland security. Mass Spectrometer Designs The first mass spectrographs were invented almost 100 years ago, by A.J. Dempster, F.W. Aston and others, and have therefore been in continuous development over a very long period. However the principle of using electric and magnetic fields to accelerate and establish the trajectories of ions inside the spectrometer according to their mass/charge ratio is common to all the different designs. The following description of Dempster’s original mass spectrograph is a simple illustration of these physical principles: The magnetic sector spectrograph PUMP F DD S S3 1 r S2 Fig. 1: Dempster’s Mass Spectrograph (1918). Atoms/molecules are first ionized by electrons emitted from the hot filament (F) and then accelerated towards the entrance slit (S1). The ions then follow a semicircular trajectory established by the Lorentz force in a uniform magnetic field. The radius of the trajectory, r, is defined by three slits (S1, S2, and S3). Ions with this selected trajectory are then detected by the detector D. How the magnetic sector mass spectrograph works: Equating the Lorentz force with the centripetal force gives: qvB = mv2/r (1) where q is the charge on the ion (usually +e), B the magnetic field, m is the mass of the ion and r the radius of the ion trajectory. -
From the Atomic to the Femtoscale Linda Young Argonne National
From the Atomic to the Femtoscale Linda Young Argonne National Laboratory, Argonne, Illinois 60439 Abstract: Atom traps of lithium can be used to provide a new window on few-body atomic and nuclear systems. The trapped atoms form an excellent sample, dense and motionless, for precision measurements. This talk describes experiments using ultracold lithium atoms to study ionization dynamics (a persistent few-body dynamical problem) and outline proposed precision measurements of isotope shifts to determine charge radii of short-lived lithium isotopes (a challenging few-body nuclear physics problem). Introduction The lithium atom, with three electrons and six through eleven nucleons, is a hotbed of activity for few-body theorists in both atomic and nuclear physics. Atomic theorists have the advantage that the forces in the problem, Coulomb interactions, are well known. This advantage simplifies development of many-body techniques for both structure and dynamics [1]. On the atomic physics side, there has been recent effort devoted both to precision calculations of atomic structure [2-5] and to understanding the dynamical correlation between the outgoing electrons in photo triple-ionization [6-9]. On the nuclear physics side, a long-standing program to calculate properties of few-body nuclei has now reached A ≤ 10 [10,11]. In these calculations, the nucleon-nucleon potentials are adjusted to fit the large collection of pp and np scattering data. Impressively, the calculations have fit the binding energies of all A ≤ 10 nuclei to an rms deviation of ≈400 keV, predicted the absence of stable A=5, 8 nuclei [12], and simultaneously predicted rms proton radii, rms neutron radii, quadrupole moments and magnetic moments. -
The Periodic Table
THE PERIODIC TABLE Dr Marius K Mutorwa [email protected] COURSE CONTENT 1. History of the atom 2. Sub-atomic Particles protons, electrons and neutrons 3. Atomic number and Mass number 4. Isotopes and Ions 5. Periodic Table Groups and Periods 6. Properties of metals and non-metals 7. Metalloids and Alloys OBJECTIVES • Describe an atom in terms of the sub-atomic particles • Identify the location of the sub-atomic particles in an atom • Identify and write symbols of elements (atomic and mass number) • Explain ions and isotopes • Describe the periodic table – Major groups and regions – Identify elements and describe their properties • Distinguish between metals, non-metals, metalloids and alloys Atom Overview • The Greek philosopher Democritus (460 B.C. – 370 B.C.) was among the first to suggest the existence of atoms (from the Greek word “atomos”) – He believed that atoms were indivisible and indestructible – His ideas did agree with later scientific theory, but did not explain chemical behavior, and was not based on the scientific method – but just philosophy John Dalton(1766-1844) In 1803, he proposed : 1. All matter is composed of atoms. 2. Atoms cannot be created or destroyed. 3. All the atoms of an element are identical. 4. The atoms of different elements are different. 5. When chemical reactions take place, atoms of different elements join together to form compounds. J.J.Thomson (1856-1940) 1. Proposed the first model of the atom. 2. 1897- Thomson discovered the electron (negatively- charged) – cathode rays 3. Thomson suggested that an atom is a positively- charged sphere with electrons embedded in it. -
Good Practice Guide for Isotope Ratio Mass Spectrometry, FIRMS (2011)
Good Practice Guide for Isotope Ratio Mass Spectrometry Good Practice Guide for Isotope Ratio Mass Spectrometry First Edition 2011 Editors Dr Jim Carter, UK Vicki Barwick, UK Contributors Dr Jim Carter, UK Dr Claire Lock, UK Acknowledgements Prof Wolfram Meier-Augenstein, UK This Guide has been produced by Dr Helen Kemp, UK members of the Steering Group of the Forensic Isotope Ratio Mass Dr Sabine Schneiders, Germany Spectrometry (FIRMS) Network. Dr Libby Stern, USA Acknowledgement of an individual does not indicate their agreement with Dr Gerard van der Peijl, Netherlands this Guide in its entirety. Production of this Guide was funded in part by the UK National Measurement System. This publication should be cited as: First edition 2011 J. F. Carter and V. J. Barwick (Eds), Good practice guide for isotope ratio mass spectrometry, FIRMS (2011). ISBN 978-0-948926-31-0 ISBN 978-0-948926-31-0 Copyright © 2011 Copyright of this document is vested in the members of the FIRMS Network. IRMS Guide 1st Ed. 2011 Preface A few decades ago, mass spectrometry (by which I mean organic MS) was considered a “black art”. Its complex and highly expensive instruments were maintained and operated by a few dedicated technicians and its output understood by only a few academics. Despite, or because, of this the data produced were amongst the “gold standard” of analytical science. In recent years a revolution occurred and MS became an affordable, easy to use and routine technique in many laboratories. Although many (rightly) applaud this popularisation, as a consequence the “black art” has been replaced by a “black box”: SAMPLES GO IN → → RESULTS COME OUT The user often has little comprehension of what goes on “under the hood” and, when “things go wrong”, the inexperienced operator can be unaware of why (or even that) the results that come out do not reflect the sample that goes in. -
TEK 8.5C: Periodic Table
Name: Teacher: Pd. Date: TEK 8.5C: Periodic Table TEK 8.5C: Interpret the arrangement of the Periodic Table, including groups and periods, to explain how properties are used to classify elements. Elements and the Periodic Table An element is a substance that cannot be separated into simpler substances by physical or chemical means. An element is already in its simplest form. The smallest piece of an element that still has the properties of that element is called an atom. An element is a pure substance, containing only one kind of atom. The Periodic Table of Elements is a list of all the elements that have been discovered and named, with each element listed in its own element square. Elements are represented on the Periodic Table by a one or two letter symbol, and its name, atomic number and atomic mass. The Periodic Table & Atomic Structure The elements are listed on the Periodic Table in atomic number order, starting at the upper left corner and then moving from the left to right and top to bottom, just as the words of a paragraph are read. The element’s atomic number is based on the number of protons in each atom of that element. In electrically neutral atoms, the atomic number also represents the number of electrons in each atom of that element. For example, the atomic number for neon (Ne) is 10, which means that each atom of neon has 10 protons and 10 electrons. Magnesium (Mg) has an atomic number of 12, which means it has 12 protons and 12 electrons. -
Centripetal Force Is Balanced by the Circular Motion of the Elctron Causing the Centrifugal Force
STANDARD SC1 b. Construct an argument to support the claim that the proton (and not the neutron or electron) defines the element’s identity. c. Construct an explanation based on scientific evidence of the production of elements heavier than hydrogen by nuclear fusion. d. Construct an explanation that relates the relative abundance of isotopes of a particular element to the atomic mass of the element. First, we quickly review pre-requisite concepts One of the most curious observations with atoms is the fact that there are charged particles inside the atom and there is also constant spinning and Warm-up 1: List the name, charge, mass, and location of the three subatomic circling. How does atom remain stable under these conditions? Remember particles Opposite charges attract each other; Like charges repel each other. Your Particle Location Charge Mass in a.m.u. Task: Read the following information and consult with your teacher as STABILITY OF ATOMS needed, answer Warm-Up tasks 2 and 3 on Page 2. (3) Death spiral does not occur at all! This is because the centripetal force is balanced by the circular motion of the elctron causing the centrifugal force. The centrifugal force is the outward force from the center to the circumference of the circle. Electrons not only spin on their own axis, they are also in a constant circular motion around the nucleus. Despite this terrific movement, electrons are very stable. The stability of electrons mainly comes from the electrostatic forces of attraction between the nucleus and the electrons. The electrostatic forces are also known as Coulombic Forces of Attraction. -
Of the Periodic Table
of the Periodic Table teacher notes Give your students a visual introduction to the families of the periodic table! This product includes eight mini- posters, one for each of the element families on the main group of the periodic table: Alkali Metals, Alkaline Earth Metals, Boron/Aluminum Group (Icosagens), Carbon Group (Crystallogens), Nitrogen Group (Pnictogens), Oxygen Group (Chalcogens), Halogens, and Noble Gases. The mini-posters give overview information about the family as well as a visual of where on the periodic table the family is located and a diagram of an atom of that family highlighting the number of valence electrons. Also included is the student packet, which is broken into the eight families and asks for specific information that students will find on the mini-posters. The students are also directed to color each family with a specific color on the blank graphic organizer at the end of their packet and they go to the fantastic interactive table at www.periodictable.com to learn even more about the elements in each family. Furthermore, there is a section for students to conduct their own research on the element of hydrogen, which does not belong to a family. When I use this activity, I print two of each mini-poster in color (pages 8 through 15 of this file), laminate them, and lay them on a big table. I have students work in partners to read about each family, one at a time, and complete that section of the student packet (pages 16 through 21 of this file). When they finish, they bring the mini-poster back to the table for another group to use. -
Mass Defect & Binding Energy
Sem-3 CC7 Nuclear Physics Mass Defect & Binding Energy According to nuclear particle experiments, the total mass of a nucleus (mnuc) is less than the sum of the masses of its constituent nucleons (protons and neutrons). For a nucleus with Z protons and mass number A, the mass difference or mass defect is given by Δm= Zmp + (A−Z)mn − mnuc where Zmp is the total mass of the protons, (A−Z)mn is the total mass of the neutrons, and mnuc is the mass of the nucleus. According to Einstein’s special theory of relativity, mass is a measure of the total energy of a system (E=mc2). The energy equivalent to mass defect is alled the binding energy B of the nucleus. Thus 2 B= [Zmp + (A−Z)mn − mnuc] c The binding energy is equal to the amount of energy released in forming the nucleus. Example 1. Calculate the mass defect and the binding energy of the deuteron. The mass of the −27 deuteron is mD=3.34359×10 kg or 2.014102u. Solution For the deuteron Z=1 and A=2. The mass defect for the deuteron is Δm=mp+mn−mD=1.008665 u+ 1.007825 u- 2.014102u = 0.002388u The binding energy of the deuteron is then B= Δm c2= Δm ×931.5 MeV/u=2.224MeV. Over two million electron volts are needed to break apart a deuteron into a proton and a neutron. This very large value indicates the great strength of the nuclear force. By comparison, the greatest amount of energy required to liberate an electron bound to a hydrogen atom by an attractive Coulomb force (an electromagnetic force) is about 10 eV. -
Iron-57 of Its Isotopes and Has an Sum of Protons + Neutrons 26 Fe Average Mass As Determined by a in the Nucleus
Elements - elements are pure homogeneous forms of matter Solid Liquid Gas Plamsa •constant volume & shape •constant volume but takes •varaible shape and volume •like a gas except it •very low compressibility on the shape of container that fills the container is composed of ions; •particles vibrate in place •low compressibility •high compressibility an ion is charged •highly ordered arrangement •random particle movement •complete freedom of motion atom or group of •do not flow or diffuse •moderate disorder •extreme disorder atoms. •strongest attractive forces •can flow and diffuse •flow and diffuse easily •examples: between particles •weaker attractive forces •weakest attractive forces - flames •generally more dense than •more dense than gases •least dense state - atmosphere of stars liquids •exert a pressure easily - a comet's tail Matter NO YES Pure Substance Can it be separated Mixture by physical means? Can it be decomposed by Is the mixture composition ordinary chemical means? identical throughout; uniform? NO YES YES NO element compound homogeneous heterogenous mixture mixture Co,Fe,S,H,O,C FeS, H2O, H2SO4 steel, air, blood, steam, wet iron, solution of sulfuric acid Cannot be separated Can be decomposed and rust on steel chemcially into simple chemcially separated Uniform appearance, Appearance, composition, substances into simple substances. composition and and properties are variable properties throughout in different parts of the sample Isotopes Is a mass number attached to the element? NO YES All atoms of the same element are not exactly alike mass number attached mass number equals the 57 The element is as a mixture also can be written as iron-57 of its isotopes and has an sum of protons + neutrons 26 Fe average mass as determined by a in the nucleus.