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Atomic Physics -4 § 1.1 Historical perspective 1895 1896 The discovery of X-rays Discovery of radioactivity Röntgen Becquerel 4 + U →234 Th 90 2 He 238 92 1897 1900 1905 1911 1912 1913 1919 1920 The discovery of electron The discovery of the black body radiation formula The development of the theory of special relativity Rutherford’s atomic model Discovery of isotopes Bohr’s theory of the hydrogen atom Induced nuclear transmutation The radii of a few heavy nuclei ~ 10-14 m = 10 F << 10-10 m J.J. Thomson Max Planck Albert Einstein Rutherford J.J. Thomson Niels Bohr J.J. Thomson Chadwick 1928 Alpha decay Gamow, Gurney and Condon 1932 Discovery of neutron Chadwick 1932 n-p hypothesis Heisenberg 1932 Discovery of positron Anderson 1934 Beta decay Enrico Fermi 1935 Roles of mesons in nuclear forces Yukawa 1936 Discovery of μ meson Anderson and Neddermeyer 1946 Discovery of π meson Powell 1956 Non-conservation of parity in beta decay Lee, Yang and 吳健雄教授 Atomic Physics The physics of the electronic, extra-nuclear structure of Nuclear Physics The physics of the atomic nucleus, believed to be constituted of neutrons and protons Elementary Particle Physics The physics of quarks and gluons, believed to be the constituents of protons and neutrons, and of leptons and gauge bosons and… who knows what else! Quarks, gluons, leptons, and gauge bosons are believed to have no substructure. atoms Characteristics of types of radiation Radioactivity (Spontaneous emission of radiation) Type Alpha particle Beta particle Positron Gamma ray Symbol Charge Mass (amu) 2+ 4.002 60 0 e -1 1- 0.000 548 6 0 e +1 1+ 0.000 548 6 0 0 He β or β or γ Types of Radiation The three most common types of radiation are alpha (α), beta (β), and gamma (γ). The Discovery of Atomic Structure Radioactivity The Discovery of Atomic Structure Radioactivity A high deflection towards the positive plate corresponds to radiation which is negatively charged and of low mass. This is called β-radiation (consists of electrons). No deflection corresponds to neutral radiation. This is called γ-radiation. Small deflection towards the negatively charged plate corresponds to high mass, positively charged radiation. This is called α-radiation (He nuclei). Two isotopes of Helium or Na-23 or Na-24 Isotope: one of two or more atoms having the same number of protons but different numbers of neutrons Atomic Number Atoms are composed of identical protons, neutrons, and electrons How then are atoms of one element different from another element? Elements are different because they contain different numbers of PROTONS The “atomic number” of an element is the number of protons in the nucleus # protons in an atom = # electrons Atomic Number Atomic number (Z) of an element is the number of protons in the nucleus of each atom of that element. Element # of protons Atomic # (Z) Carbon 6 6 Phosphorus 15 15 Gold 79 79 Mass Number Mass number is the number of protons and neutrons in the nucleus of an isotope: Mass # = p+ + n0 p+ n0 e- Mass # 8 10 8 18 Arsenic - 75 33 42 33 75 Phosphorus - 31 15 16 15 31 Nuclide Oxygen - 18 Complete Symbols Contain the symbol of the element, the mass number and the atomic number. Superscript → Mass number Subscript → Atomic number X A X Z Complete Symbols Symbol A = Mass number(equal to the no. of proton + no. of neutron) Z = Atomic number (equal to the no. of protons, therefore, equal to the no. of electrons) Contain the symbol of the element, the mass number and the atomic number. 1 H 1 A=1 Z=1 p=1 e=1 n=0 16 O 8 A = 16 Z=8 p=8 e=8 n=8 Symbols Find each of these: a) number of protons b) number of neutrons c) number of electrons d) Atomic number e) Mass Number 80 35 Br Symbols If an element has an atomic number of 34 and a mass number of 78, what is the: a) number of protons b) number of neutrons c) number of electrons d) complete symbol Symbols If an element has 91 protons and 140 neutrons what is the a) Atomic number b) Mass number c) number of electrons d) complete symbol Symbols If an element has 78 electrons and 117 neutrons what is the a) Atomic number b) Mass number c) number of protons d) complete symbol Practice – Complete the table 27 13 Al Practice – Complete the table 13 6C 96 42 Mo 27 13 Al 133 55 Cs Tro: Chemistry: A Molecular Approach, 2/e No change occurs inside a nucleus in chemistry Atoms can lose or gain electrons Na − e− Na+ positive ion = cation Mg − 2e− Mg2+ Cl + e− Cl− O + 2e− O2− negative ion = anion Practice – Complete the table Al 3+ Practice – Complete the table S 2− 2+ Mg Al3 + Br Tro: Chemistry: A Molecular Approach, 2/e − Symbol Number of Number of Number of Protons in Neutrons Net charge Electrons Nucleus in Nucleus 87Rb+ 16 18 36 2− 28 1+ Symbol Number of Number of Number of Protons in Neutrons Net charge Electrons Nucleus in Nucleus 87Rb+ 37 50 36 1+ 32S2− 16 18 18 2− 65Cu+ 29 36 28 1+ Isotopes Dalton was wrong about all elements of the same type being identical Atoms of the same element can have different numbers of neutrons. Thus, different mass numbers. These are called isotopes. Isotopes Frederick Soddy (1877-1956) proposed the idea of isotopes in 1912 Isotopes are atoms of the same element having different masses, due to varying numbers of neutrons. Soddy won the Nobel Prize in Chemistry in 1921 for his work with isotopes and radioactive materials. Isotopes Adding neutrons to a nucleus (or taking them away) does not affect the nuclear charge (or number of electrons) so chemically the atom is not different It does affect the nuclear properties (stability etc ) - specify an element by Z - specify an isotope by A a complete description requires both Z is implied by the historical name eg 14C A = 14 Z = 6 - carbon with 2 extra neutrons Hydrogen Deuterium Tritium p+e p+n+e p+n+n+e 1 1 1 1H 2H 3H (in heavy water) These are all isotopes of hydrogen but are not separate elements they have the same chemical properties but different nuclear properties (therefore things like nuclear burning in stars are different). Naming Isotopes We can also put the mass number after the name of the element: carbon-12 carbon-14 uranium-235 Isotopes are atoms of the same element having different masses, due to varying numbers of neutrons. Isotope Protons Electrons Neutrons Hydrogen–1 (protium) 1 1 0 Hydrogen-2 (deuterium) 1 1 1 1 1 2 Hydrogen-3 (tritium) Nucleus Isotopes Elements occur in nature as mixtures of isotopes. Isotopes are atoms of the same element that differ in the number of neutrons. Atomic Weights Weighted average of the masses of the constituent isotopes Lower number on periodic chart How do we know what the values of these numbers are? Measuring Atomic Mass --the Mass Spectrometer The mass spectrometer can be used to determine the atomic mass of isotopes. Mass Spectrometry A mass spectrometer is a device that separates positive gaseous ions according to their mass-to-charge ratios A record of the separation of ions is called a mass spectrum Mass Spectrometer If a stream of positive ions having equal velocities is brought into a magnetic field, the lightest ions are deflected the most, making a tighter circle Mass Spectrum of Neon The mass spectrum neon shows three isotopes with the isotope at atomic mass = 20 accounting for more than 90% of neon. Mass Spectrum of Germanium The mass spectrum of germanium shows 5 peaks at relative atomic masses of 70, 72,73,74, and 75 Atomic Mass Actual masses of individual atoms are small and impractical to work with. It is more useful to compare the relative masses of atoms using a reference isotope as a standard The carbon-12 atom was assigned a mass of exactly 12 atomic mass units. Atomic mass unit (amu) – one twelfth of the mass of carbon-12 atom. Atomic Mass Units An atomic mass unit (amu) is equal to exactly 1/12 of the mass of an atom of Carbon 12. One atomic mass unit is equal to 1.66054 x 10-24 grams. Note that this is slightly less than the mass of a proton or a neutron. An atomic mass unit is sometimes called a Dalton (D). 1.00 g = 6.02214 x 1023 amu. This number is also known as Avogadro’s Number and it defines the size of a quantity we call a mole. Atomic Mass How heavy is an atom of oxygen? It depends, because there are different kinds of oxygen atoms. We are more concerned with the average atomic mass. This is based on the abundance (percentage) of each variety of that element in nature. We don’t use grams for this mass because the numbers would be too small. Measuring Atomic Mass Instead of grams, the unit we use is the Atomic Mass Unit (amu) It is defined as one-twelfth the mass of a carbon-12 atom. Carbon-12 chosen because of its isotope purity. Each isotope has its own atomic mass, thus we determine the average from percent abundance. To calculate the average: Multiply the atomic mass of each isotope by it’s abundance (expressed as a decimal), then add the results. Atomic Masses Atomic mass is the average of all the naturally occurring isotopes of that element. Isotope Symbol Carbon-12 12C Carbon-13 13C Carbon-14 14C Composition of the nucleus 6 protons 6 neutrons 6 protons 7 neutrons 6 protons 8 neutrons Carbon = 12.011 % in nature 98.89% 1.11% <0.01% Question Knowns and Unknown Solution Answer 1H 1.6735 x 10−24 g 16O 2.6560 x 10−23 g One atomic mass unit (amu) is defined as 1/12 of the mass of a 12C atom. 12C atom: 6 protons, 6 neutrons, 6 electrons. 1 amu = 1.6605 x 10−24 g 1H 1.6735 x 10−24 g 16O 2.6560 x 10−23 g 1 amu = 1.6605 x 10−24 g 1.6735 × 10 − 24 1 amu g× = 1.0078 amu − 24 1.6605 × 10 g 1 amu 2.6560 × 10 g × 15.995 amu = −24 1.6605 × 10 g −23 Calculating the average relative atomic mass The average atomic mass that is shown in the periodic table is really the weighted average of the atomic masses of each of the elements isotopes. Germanium has 5 isotopes whose relative atomic masses are shown in the table Mass Number 70 72 73 74 75 % Abundance 20.55 27.37 7.67 36.74 7.67 Calculating the Average Relative Atomic Mass To calculate the average atomic mass multiply the atomic mass of each isotope by its abundance (expressed as a decimal fraction) Mass Number 70 72 73 74 75 % Abundance 20.55 27.37 7.67 36.74 7.67 Average atomic mass = (0.2055)(70) + (0.2737)(72) + (0.0767)(73) + (0.3674)(74)+ (0.0767)(75) = 72.36 Note: atomic masses are ratios so they do not have real units although they are sometimes called atomic mass units or amu Lithium has two naturally occurring isotopes. Lithium-6 has an atomic mass of 6.015 amu; lithium-7 has an atomic mass of 7.016 amu. The atomic mass of lithium is 6.941 amu. What is the Percentage of naturally occurring lithium-7? 7.016x + 6.015(1-x) = 6.941 1.001x = 0.926 x=(.925)(100%) = 92.5% A note on natural abundances of nuclides: Elements with an even number of neutrons are more abundant than elements with an odd number of neutrons. Elements with an even number of protons and an even number of neutrons are more abundant than elements with an odd number of protons and an even number of neutrons. Moles A mole is the amount of substance that contains as many particles as there atoms in exactly 12g of carbon-12. It’s a counting unit (like a dozen) The number of particles in one mole of a pure substance is Avogadro’s number 6.022 x 1023 Molar mass – the mass of one mole of a pure substance is its molar mass. Using a mass spectrometer, scientists determined that the mass of one hydrogen atom (about 1 “atomic mass unit”) is 1.6605 x 1024 gram. This means that there are 6.0223 x 1023 “amu” in 1.0000 g. Or 6.0223 x 1023 hydrogen atoms in 1.0000 g. We define 6.0223 x 1023 atoms of any element to be “one mole” of that element. It follows that: one mole of He atoms (each 4 amu) = 4 grams He. one mole of C atoms (each 12 amu) = 12 grams C. Generalizing: The atomic mass of any element = the number of grams in one mole of that element. That is, the larger, non-integral number for each element in the periodic table is the element’s “grams per mole.” Exceptions: elements whose atoms “pair up” to form molecules. H2, O2, N2, F2, Cl2, Br2, I2 In this case, one mole = 6.0223 x 1023 molecules, not atoms. So one mole of hydrogen is one mole of H2 molecules = 2 grams, not 1 gram. How is the mole useful to chemists? Take, for example, the compound iron sulfide, FeS. The formula tells us that any amount of FeS contains equal numbers of Fe and S atoms. So suppose I have some iron and some sulfur and want to make 100 g of FeS. If I want equal numbers of Fe and S atoms, then I want equal numbers of moles of Fe and S atoms. Going to the Periodic Table, I see that 55.85 g Fe is one mole, and 32.06g S is one mole. If I use these amounts I will have 55.85 + 32.06 = 87.91 g FeS (Law of Conservation of Matter.) Scaling up, I can combine 63.53g Fe + 36.47g S to get 100g FeS. By understanding the mole, I accomplished two things: 1. I did not waste any Fe or S. 2. I produced pure FeS, not a mixture of FeS and some leftover Fe or S. Einstein – Energy/Mass Equivalence In 1905, Albert Einstein published a 2nd major theory called the Energy-Mass Equivalence in a paper called, “Does the inertia of a body depend on its energy content?” Energy Unit Check 2 m EB = ∆mc → Joule = kg × 2 s W = Fx → Joule = Nm m Fnet = ma → N = kg × 2 s 2 m m E = W = kg × 2 × m = kg × 2 s s 2 Mass Defect The nucleus of the atom is held together by a STRONG NUCLEAR FORCE. The more stable the nucleus, the more energy needed to break it apart. Energy need to break the nucleus into protons and neutrons is called the Binding Energy Einstein discovered that the mass of the separated particles is greater than the mass of the intact stable nucleus to begin with. This difference in mass (∆m) is called the mass defect. Mass Defect - Explained The extra mass turns into energy holding the atom together. Mass Defect – Example A Ton of TNT For some reason, the comparison unit for nuclear explosions which became most popular was the "ton of TNT". A nominal energy release for a ton of TNT can be extracted from general statements about nuclear weapons. One of those is "one kilogram of mass converted to energy is equivalent to about 22 megatons of TNT". From the Einstein equation, the conversion is mc2 = (1kg)c2 = 9E16 Joules = 22 megatons TNT mc2 = (0.001kg)c2 = 9E13 J = 22 kilotons This is consistent with the oft-quoted statement that the 20 kiloton Hiroshima bomb converted about 1 gram of mass to energy. Paths of Radioactive Decay Nucleosynthesis After the creation of the universe, energy had transformed into matter in accordance with Einstein’s equation E = mc2. The first types of matter to form were the smallest fundamental particles: electrons, and quarks. Quarks are particles that combine to form neutrons and protons. Nucleosynthesis is the fusing of fundamental and subatomic particles to create atomic nuclei. Fusion of Hydrogen and the Mass Defect protons 4 2He Positrons 4 11H 4 2He + 01 e Binding energy of the 42He nucleus • 2 neutrons + 2 protons: 2 x 1.67494E-24 + 2 x 1.67263E-24 = 6.69513E-24 g • Subtract the actual mass of the nucleus: 6.69513E-24 – 6.64465E-24 = 5.048E-24 g • This is the mass defect. • E = (∆m)c2 • (5.048E-29 kg) x (2.998E8 m/s)2 = 4.537E-12 kg (m/s)2 • or 4.537E-12 J (Joules) = Binding energy for helium-4 For the reaction: H2(g) + ½ O2(g) → H2O(l) the energy released is 4.7E-19 J per H2 molecule. The mass of a stable nucleus is always less than the mass of the individual particles that make up the nucleus. This is known as the mass defect (∆m). The larger the mass defect the stronger the energy that binds the nuclear particles together. The binding energy (E) can be calculated by substituting the mass defect into Einstein's equation for the relationship between mass and energy: E = mc2 to become E = (∆m)c2 Periodic Table Periodic Table – an arrangement of elements in which the elements are separated into groups based on a set of repeating properties. Do You Understand Isotopes? How many protons, neutrons, and electrons are in 14 6 C 11 6 C? ? 6 protons, 8 (14 - 6) neutrons, 6 electrons How many protons, neutrons, and electrons are in 6 protons, 5 (11 - 6) neutrons, 6 electrons Compton effect Elastic scattering of massless photon with electron (initially at rest) particle nature of photon § 1.5 The nuclear constituents Notation used to represent a given nuclide Z: atomic number A: atomic mass number N: neutron number A Z XN A= Z +N X: chemical symbol M ≈ integer × M H M: the mass of a specific atom MH: the mass of a hydrogen atom Mendeleev’s Periodic Table Dmitrii I. Mendeleev arranged elements in the periodic table by their chemical and physical properties. He left open spaces in his periodic table to account for elements not yet discovered. The Modern Periodic Table The modern periodic table is also based on a classification of elements in terms of their physical and chemical properties. The horizontal rows are called periods. Columns contain elements of the same family or group. Transition metals are the elements in group 3 through 12 in the periodic table. Groups of Elements Group 1 contains the alkali metals. Group 2 contains the alkaline earth metals. Group 17 contains the halogens. Broad Categories of Elements Metals are elements on the left-hand side of the table. Metals are shiny solids that conduct heat and electricity well and are malleable and ductile. Nonmetals have properties opposite to those of the metals and are on the right side of table Metalloids are the elements between the metals and nonmetals. Continued Main group elements or representative elements are the elements in groups 1,2 and 13 through 18. The noble gases are the elements in Group 18. Kinds of Compounds Molecular Compounds are composed of atoms held together by covalent bonds. Covalent bonds are shared pairs of electrons that chemically bond atoms together. Ionic Compounds are composed of positively and negatively charged ions that are held together by electrostatic attraction. Ions with negative charge are called anions. Ions with positive charge are called cations. Periodic Table Each element is identified by its symbol place in a square. The atomic number of the element is shown centered above the symbol. Elements are listed in order of increasing atomic number, from left to right and from top to bottom. Period - each horizontal row of the periodic table. Within a given period, the properties of the elements vary as you move across it from element to element. Group – each vertical column of the periodic table. Elements within a group have similar chemical and physical properties. Each group is identified by a number and the letter A or B. Noble Gas Halogen Group Alkali Metal Alkali Earth Metal Period A molecule is an aggregate of two or more atoms in a definite arrangement held together by chemical bonds H2 H2O NH3 A diatomic molecule contains only two atoms H2, N2, O2, Br2, HCl, CO A polyatomic molecule contains more than two atoms O3, H2O, NH3, CH4 CH4 An ion is an atom, or group of atoms, that has a net positive or negative charge. cation – ion with a positive charge If a neutral atom loses one or more electrons it becomes a cation. Na 11 protons 11 electrons Na+ 11 protons 10 electrons Cl- 17 protons 18 electrons anion – ion with a negative charge If a neutral atom gains one or more electrons it becomes an anion. Cl 17 protons 17 electrons A monatomic ion contains only one atom Na+, Cl-, Ca2+, O2-, Al3+, N3- A polyatomic ion contains more than one atom OH-, CN-, NH4+, NO3- Do You Understand Ions? How many protons and electrons are in 27 3+ ? 13 Al 13 protons, 10 (13 – 3) electrons How many protons and electrons are in 34 protons, 36 (34 + 2) electrons 78 Se 234 ? A molecular formula shows the exact number of atoms of each element in the smallest unit of a substance An empirical formula shows the simplest whole-number ratio of the atoms in a substance molecular empirical H2O H2O C6H12O6 CH2O O3 O N2H4 NH2 Ionic compounds consist of a combination of cations and an anions • the formula is always the same as the empirical formula • the sum of the charges on the cation(s) and anion(s) in each formula unit must equal zero The ionic compound NaCl Formula of Ionic Compounds 2 x +3 = +6 3 x -2 = -6 Al2O3 Al3+ O21 x +2 = +2 2 x -1 = -2 CaBr2 Ca2+ Br1 x +2 = +2 1 x -2 = -2 Na2CO3 Na+ CO32- Some Polyatomic Ions NH4+ ammonium SO42- sulfate carbonate 2SO3 sulfite HCO3 bicarbonate NO3 nitrate ClO3- chlorate NO2- nitrite Cr2O72- dichromate SCN- thiocyanate CrO42- chromate OH- hydroxide CO3 2- Chemical Nomenclature Ionic Compounds often a metal + nonmetal anion (nonmetal), add “ide” to element name BaCl2 barium chloride K2O potassium oxide Mg(OH)2 magnesium hydroxide KNO3 potassium nitrate Transition metal ionic compounds indicate charge on metal with Roman numerals FeCl2 2 Cl- -2 so Fe is +2 iron(II) chloride FeCl3 3 Cl- -3 so Fe is +3 iron(III) chloride Cr2S3 3 S-2 -6 so Cr is +3 (6/2) chromium(III) sulfide Molecular compounds nonmetals or nonmetals + metalloids common names H2O, NH3, CH4, C60 element further left in periodic table is 1st element closest to bottom of group is 1st if more than one compound can be formed from the same elements, use prefixes to indicate number of each kind of atom last element ends in ide Molecular Compounds HI hydrogen iodide NF3 nitrogen trifluoride SO2 sulfur dioxide N2Cl4 dinitrogen tetrachloride NO2 nitrogen dioxide N2O dinitrogen monoxide TOXIC! Laughing Gas An acid can be defined as a substance that yields hydrogen ions (H+) when dissolved in water. HCl •Pure substance, hydrogen chloride •Dissolved in water (H+ Cl-), hydrochloric acid An oxoacid is an acid that contains hydrogen, oxygen, and another element. HNO3 nitric acid H2CO3 carbonic acid H2SO4 sulfuric acid A base can be defined as a substance that yields hydroxide ions (OH-) when dissolved in water. NaOH sodium hydroxide KOH potassium hydroxide Ba(OH)2 barium hydroxide Most common charges on ions. Note elements within a Group (column) typically have the same charge. Are these charges consistent with the most stable electron configurations? Continued Molecular compounds are made of nonmetals Ionic compounds are made of a metal and a nonmetal. Metal form cations and nonmetals form anions. Naming Compounds Binary Molecular Compounds Compounds consisting of two nonmetals First element in the formula is named first. Second element is named by changing the elemental name ending to ide. Use prefixes to identify quantity of atoms. Mono-1, di-2, tri-3, tetra-4, penta-5, hexa-6, hepta-7, octa-8, nona-9, deca-10 Never use the prefix mono- P2O5 = diphosphorus pentoxide Compounds and Earth’s Early Atmosphere Carbon Dioxide Water (dihydrogen monoxide) Sulfur Dioxide Sulfur Trioxide Nitrogen Oxide Nitrogen Dioxide Naming…Binary molecular compounds CO CO2 NO NO3 SO2 SO3 Practice Name the following compounds or give the correct chemical formula. 1. 2. 3. 4. Tetraphosphorus decoxide CCl4 P2N5 Sulfur trioxide Binary Ionic Compounds Binary ionic compounds consist of cations (usually metals) and anions (usually nonmetals). Binary Ionic Compounds The cation is named first using the elemental name. If the metal can form cations with different charges then a Roman numeral is added to indicate the charge of the cation. The anion is named with the ide ending. The formulas for ionic compounds must always be neutral. Practice Write the name or chemical formula for the following compounds. 1. 2. 3. 4. NaCl CrCl3 Zinc nitride Copper(I) oxide Polyatomic Ions Acetate C2H3O2Carbonate CO32Perchlorate ClO4Nitrate NO3Sulfate SO42Chromate CrO42Examples from Table 2.3 on page 64 Practice Write the names or chemical formulas for the following compounds. 1. 2. 3. 4. Cr(ClO4)3 NH4NO3 Lithium bicarbonate Calcium hypobromite Nomenclature Give the chemical names for the following ionic compounds: a. NiCO3 b. NaCN c. LiHCO3 d. Ca(ClO)2 Give the formula and charge of the oxoanion of each of the following a. Potassium tellurite b. sodium arsenate c. Calcium selenite d. potassium chlorate Naming Binary Acids Binary acids contain hydrogen and a halogen atom. The names of these acids are contain the halogen base name with the prefix, “hydro,” and suffix, “ic,” and the word acid. Example HBr - hydrobromic acid Oxy Anions & Related Acids Anion Anion Name Acid HClO Acid Name ClO-Hypochlorite Hypochlorous acid ClO2- Chlorite HClO2 Chlorous acid ClO3- Chlorate HClO3 Chloric acid ClO4- Perchlorate HClO4 Perchloric acid Periodic Table What distinguishes the atoms from one element from the atoms of another? The number of protons What equation tells you how to calculate the number of neutrons in an atom? Mass number – atomic number = # of neutrons. How do the isotopes of a given element differ from one another? Different mass number and different numbers of neutrons. Periodic Table What makes the periodic table such a useful tool? It allows you to compare the properties of the elements What does the number represent in the isotope platinum194? Write the symbol from this atom using superscripts and subscripts. It represents the mass number 194 78 Pt Periodic Table Name the elements that have properties similar to those of the element calcium (Ca). Beryllium (Be), magnesium (Mg), strontium (Sr), Barium (Ba), radium (Ra) 194 Consider Pt how would changing the value of the 78 subscript change the chemical properties of the atom? The subscript is the number of protons in atoms of the isotope. Changing the number of protons would change the chemical identity of the isotope to that of another element. Displacement Law (by Russel, by Soddy and Fajans) 1. The emission of an α-particle reduces the atomic mass by 4 and the atomic number by 2. 2. The emission of a β-particle increases the atomic number by 1 and leaves the mass number unchanged. α-rays An α particle, or a helium nucleus, is composed of two protons and two neutrons, totally four nucleons. It carries +2e charge and has strong capability of ionization. When α particles passing through materials high density of ions are created in a cylindrical shape along the path. It is called the “cylindrical ionization”. High energy α particles lose their energy fast and can only travel through a short distance. Ex. 210 84 Po (polonium) emits 5.3 MeV α-partilces @ Alpha particles with 5.3 MeV is able to penetrate through 3.8 cm thickness of air. @ A piece of paper of common thickness is able to stop those alpha particles. @ They can not penetrate through human skin. β-rays Beta rays (electrons) interact with atoms. They lose energy by exciting or ionizing atoms to higher energy states and free states while traveling through materials. Ion density created by electrons are far less than those from alpha particles with the same energy. Electrons can travel through a much longer distance than alpha particles. @ Electrons with 5.3 MeV is able to penetrate through 20 m thickness of air. This is roughly 500 times of alpha particles. @ Electrons with 5.3 MeV is able to penetrate through 10 mm in Al and 2 mm in Pb . @ β-rays are much more dangerous than α-rays . γ-rays Gamma rays are energetic photons. They interact with materials through three different kinds of effect. 1. Photoelectric effect Eγ < 0.4 MeV 2. Compton effect 0.4 MeV < Eγ < 5 MeV 3. Pair production effect Eγ > 5 MeV @ These effects have very small effective cross section (very small probability of occurrence) thus huge traveling distance. @ γ-rays are able to penetrate through ~ cm in Pb . @ Watch out for γ-rays . § 1.2 The Rutherford scattering formula 1. In 1906 Rutherford observed that a beam of α-particles became spread slightly on traversing a thin layer of material. A layer of material insufficient to stop α-particles (e.g. gold 4μm thick) would scatter particles an average of about 9 degrees. α- 2. In 1909 Rutherford’s colleagues, Geiger and Marsden, observed that one in a few thousand α-particles suffered a scattering of greater than 90º. Rare, Large-angle Scatters!! Massive cores were encountered. Alpha particles hit atoms with massive nucleus cores. 1. The averaged 9 degrees small angle scattering is the result of many very small angle deflections (multiple scattering). Multiple scattering: The deflection of the path is the result of the sum of many very small deflections in many atoms, all uncorrelated. 2. The rare large angle scattering is the result of a single encounter (single scattering) with an atom. Single scattering: The deflection of the path of a particle crossing a layer of material is the result of a significant deflection in one, and only one, encounter with an atom. Size of Nuclei Atomic radius of aluminum = 1.3 x 10-10 m Nuclear radius aluminum = 3.6 x 10-15 m Size Comparison Ernest Rutherford (1871- 1937) The Rutherford scattering formula Assumptions 1 The nuclear model 2 Target nucleus fixed (no recoil) 3 Point-like charges 4 Coulomb force only 5 Elastic scattering 6 Classical mechanics p = Zze / 4πε 0T 2 p distance of closest approach for b = 0 The notation for quantities used in deriving Rutherford’s formula for the differential scattering cross-section for the elastic scattering of one charged particle by a fixed charged target particle. m v T ze mass velocity kinetic energy electric charge Incident particle Ze b d u θ r, φ charge of target nucleus (at O) impact parameter distance of closest approach (at D) velocity of incident particle at D angle of scatter polar coordinates with respect to OD of point (X) on the trajectory of particle. Quantities in the figure 1. The orbit is hyperbolic and at D the incident particle is at its distance of closest approach, d . 2. The orbit is clearly symmetric about the line OD. 3. If b was zero the incident particles would approach to a distance p . At this point the incident kinetic energy is transformed into mechanical potential energy in the Coulomb field, therefore: 1 2 mv p = Zze 2 / 4πε 0 2 Step 1 To find the connection between b and θ. In this system the angular momentum about O is conserved. dϕ mvb = mr dt 2 (1) hence dt dϕ = 2 vb r (2) Consider the component of the linear momentum in the direction OD. This changes from –mvsin(θ/2) to mvsin(θ/2). The total momentum change along the OD direction is mv sin(θ / 2) − [− mv sin(θ / 2)] = 2mv sin(θ / 2) (3) At X the rate of change of this momentum is the component of the Coulomb repulsion in the direction OD. 2mv sin From equation (2) θ 2 +∞ = ∫ ( Zze 2 / 4πε 0 r 2 ) cos ϕdt −∞ dϕ dt = r vb 2 (4) put this into equation (4) then we have θ Zze 2 ϕ =(π −θ ) / 2 p mv (π −θ ) / 2 [ ] 2mv sin = cos sin ϕ ϕ ϕ d = − (π −θ ) / 2 2 4πε 0 vb ∫ϕ = − (π −θ ) / 2 2 b Finally θ p tan = 2 2b (6) (5) Step 2 To derive a first cross-section. θ p tan = 2 2b This equation means that as b decreases θ increases. To suffer an angle of scatter greater than the impact parameter b must be less than ( p / 2) cot(Θ / 2) Θ Θ To suffer an angle of scatter greater than ( p / 2) cot(Θ / 2) the impact parameter b must be less than This means the incident particle must strike a disk of this radius centered at O and perpendicular to the velocity v. The area, σ, presented by the nucleus for scattering through an angle greater than Θ is the area of this disk. That is πp 2 Θ σ (θ > Θ) = cot 4 2 2 (7) Equation (7) can also be written as 2 π Zze 2 Θ cot σ (θ > Θ) = 4 4πε 0T 2 2 The area σis called a cross-section. (8) Step 3 To obtain the angular differential cross-section. We need the cross-section per unit solid angle located at an angle θ. The element of solid angle dΩ between θand θ+dθ is given by dΩ = 2π sinθ dθ therefore dσ 1 dσ = dΩ 2π sin θ dθ The dσ/dθwe need is d σ (θ > Θ) dΘ from equation (8). Hence we obtain 2 dσ Zze 4 θ cosec = dΩ 16πε0T 2 2 (9) This is the famous Rutherford formula for the differential cross-section in Coulomb scattering. dσ dΩ θ 2 dσ Zze θ cosec 4 = dΩ 16πε0T 2 2 (9) § 1.3 The properties of the Rutherford differential cross-section 2 dσ Zze 4 θ cosec = dΩ 16πε0T 2 2 The cross-section (1) decreases rapidly with increasing angle,θ, (2) becomes infinite at θ= 0, (3) is inversely proportional to the square of the incident particles kinetic energy, T, (4) is proportional to the square of the charge of the incident particle and of the target nucleus. (9) 2 dσ Zze 2 θ cosec 4 = dΩ 16πε0T 2 (9) In the figure we have the momentum transfer q . q = 2 P sin(θ / 2) (10) 1. Greater value of q means larger electric force. Larger electric force (or field) means close collisions therefore less cross-section with larger scattering angle θ. 2. At a fixed angle the required momentum transfer will increase as does T. Thus the crosssection must decrease with increasing T. § 1.4 Examination of the assumptions 1. Neglect of nuclear recoil: this can be avoid by transforming to the center-of-mass of the collision. The formula is the same but the effective T is now the total kinetic energy in that frame and the angle of scatter and differential cross-section apply in that frame. 2. The classical approach to the orbit: a simple quantum mechanical approach using the Born approximation gives the same answer. 3. The point-like charges: data from heavy nuclei (Au, Ag, and Cu targets) are all consistent with Rutherford formula. Using targets of several light nuclei (i.e. Al) deviations from the Rutherford formula were found. The effect of nuclear interaction at short distances!! § 1.4 Examination of the assumptions (continued) 4. Absence of other forces: Short range nuclear forces and magnetic effect (because of spin) are present. 5. Elastic scattering: The α-particles used by Rutherford were not sufficiently energetic to cause a significant number of inelastic collisions. By inelastic collision it means that one or both of the particles involved in the collision event become excited or disintegrate. After Rutherford, artificial sources of more energetic α-particles became available and these certainly can cause inelastic collisions. 6. Relativistic effect: If the incoming particles are energetic enough the relativistic effect is not to be overlooked. Example: The scattering data of α-particle with energy exceeding 25MeV (Tα> 25MeV) on 92U deviate from what is predicted by the Rutherford formula. The closest distance D in the head-on collision with Tα = 25MeV is D = 10.6 F When an α-particle comes near the 92U nucleus to within 10.6 F it barely touch the surface of the nucleus. Energetic electron scattering experiments are able to probe internal structures of all nuclei. From the previous discussion it might be thought that a nucleus is comprised of electrons. This argument may well explain the β-radioactivity. A protons and N This is wrong!! If we consider the nucleus of the helium atom. In this model there will be 4 protons and 2 electrons occupy a volume of half linear dimension of about 2 fermis. Reason 1 From the uncertainty principle ∆p∆x ~ For an electron confined in a region of 2 fermis its momentum is roughly ∆p ~ 197.3 MeV/c ⋅ F = ~ 49 MeV ∆x 4 F ∆p ~ 197.3 MeV/c ⋅ F = ~ 49 MeV/c ∆x 4 F E = m 0 + ∆p 2 = 0.5112 + 49 2 ≈ 49 MeV 2 Te = E − m 0 = 49 MeV - 0.511 MeV ≈ 49 MeV where Te is electron’s kinetic energy Electrons with kinetic energies of the order of 49 MeV should remain bound only if there is a potential well at least that deep. Such a potential well would have effects on the optical spectroscopy of helium which do not exist. There is no electron in the nucleus!! Reason 2 Another reason that it is impossible for electrons to stay in a nucleus. When (A-Z) turns out to be an odd integer the model prediction of nuclei’s total angular momentum does not agree with observations. Example Consider the deuteron 2 1 H1 A = 2, and Z = 1 Model: There should be 2 protons and an electron. two protons 1 1 + 2 2 1 1 1 1 3 + + → or 2 2 2 2 2 But actually the deuteron spin is measured one electron 1 2 Possible spins of deuteron J =1 Nomenclature Nuclide A specific nuclear species, with a given proton number Z and neutron number N Isotopes Nuclides of same Z and different N Isotones Nuclides of same N and different Z Isobars Nuclides of same mass number A (A = Z + N) Isomer Nuclide in an excited state with a measurable half-life Nucleon Neutron or proton Mesons Particles of mass between the electron mass (m0) and the proton mass (MH). The best-known mesons are π mesons (≈ 270 m0), which play an important role in nuclear forces, and μ mesons (207 m0) which are important in cosmic-ray phenomena. Positron Photon Positively charged electron of mass m0 Quantum of electromagnetic radiation, commonly apparent as light, x ray, or gamma ray The Balmer Series of Hydrogen Lines In 1885, Johann Jakob Balmer (1825 - 1898), worked out a formula to calculate the positions of the spectral lines of the visible hydrogen spectrum m2 λ = 364.56 2 2 m −2 ( ) Where m = an integer, 3, 4, 5, … In 1888, Johannes Rydberg generalized Balmer’s formula to calculate all the lines of the hydrogen spectrum 1 1 1 = RH − 2 2 n2 n1 λ ( Where RH = 109677.58 cm-1 ) The Bohr Model - 1913 Niels Bohr (1885-1962) The Bohr Model – Bohr’s Postulates 1. 2. 3. 4. Spectral lines are produced by atoms one at a time A single electron is responsible for each line The Rutherford nuclear atom is the correct model The quantum laws apply to jumps between different states characterized by discrete values of angular momentum and energy The Bohr Model – Bohr’s Postulates 5. The Angular momentum is given by h p =n 2π ( ) 6. n = an integer: 1, 2, 3, … h = Planck’s constant Two different states of the electron in the atom are involved. These are called “allowed stationary states” The Bohr Model – Bohr’s Postulates 7. The Planck-Einstein equation, E = hν holds for emission and absorption. If an electron makes a transition between two states with energies E1 and E2, the frequency of the spectral line is given by hν = E1 – E2 ν = frequency of the spectral line E = energy of the allowed stationary state 8. We cannot visualize or explain, classically (i.e., according to Newton’s Laws), the behavior of the active electron during a transition in the atom from one stationary state to another Bohr’s calculated radii of hydrogen energy levels r = n2A0 r = 53 pm r = 4(53) pm = 212 pm r = 9 (53) pm = 477 pm r = 16(53) pm = 848 pm r = 25(53) pm = 1325 pm r = 36(53) pm = 1908 pm r = 49(53) pm = 2597 pm Lyman Series Balmer Series Paschen Series Brackett Series Series Series Pfund Humphrey’s The Bohr Model The energy absorbed or emitted from the process of an electron transition can be calculated by the equation: = ∆E RH ( 1 1 − 2 2 n2 n1 ) where RH = the Rydberg constant, 2.18 × 10−18 J, and n1 and n2 are the initial and final energy levels of the electron. Quantum Numbers Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies. Each orbital describes a spatial distribution of electron density. An orbital is described by a set of three quantum numbers. Quantum numbers can be considered to be “coordinates” (similar to x, y, and z coodrinates for a graph) which are related to where an electron will be found in an atom. Looking at Quantum Numbers: The Principal Quantum Number, n The principal quantum number, n , describes the energy level on which the orbital resides. The values of n are integers ≥ 0. n = 1, 2, 3, etc. Looking at Quantum Numbers: The Magnetic Quantum Number, m l Describes the orientation of an orbital with respect to a magnetic field This translates as the three-dimensional orientation of the orbital. Values of m l are integers ranging from -l to l : −l ≤ m l ≤ l. Values of l Values of ml Orbital Number of designation orbitals 0 0 s 1 1 -1, 0, +1 p 3 2 -2, -1, 0, +1, +2 d 5 3 -3, -2, -1, 0, +1, +2, +3 f 7 Quantum Numbers and Subshells Orbitals with the same value of n form a shell Different orbital types within a shell are called subshells. A Summary of Atomic Orbitals from 1s to 3d Empty subshells Valence subshells Full subshells Approximate energy levels for neutral atoms. From Ronald Rich, Periodic Correlations, 1965 Wolfgang Pauli (1900-1958) Pauli Exclusion Principle, 1925 “There can never be two or more equivalent electrons in an atom for which in strong fields the values of all quantum numbers n, k 1, k 2, m 1 (or, equivalently, n, k 1, m 1, m 1) are the same.” Hund’s Rule Friedrich Hund (1896 1997) For degenerate orbitals, the lowest energy is attained when the electrons occupy separate orbitals with their spins unpaired. J. Mauritsson, P. Johnsson, E. Mansten, M. Swoboda, T. Ruchon, A. L’Huillier, and K. J. Schafer, Coherent Electron Scattering Captured by an Attosecond Quantum Stroboscope, PhysRevLett.,100.073003, 22 Feb. 2008 http://www.atto.fysik.lth.se/ Remember… Scientists Dalton Thomson – Cathode Ray Tube Millikan – Oil dropper Apparatus Rutherford – Gold Foil Alpha Scattering Bohr Planck Einstein Models Thomson Model Rutherford Model Bohr Model Quantum Mechanical Sub-Atomic Particles Protons – positive charge, found in the nucleus. Neutrons – no charge, found in the nucleus. Electrons – negatively charged, found around the nucleus (electron cloud). Atomic Structure Isotopes – same elements but different number of neutrons. The mass number will INDIRECTLY give you the number of neutrons. Ions – charged particles. The loss of electrons gives the atom a positive charge (+). The gaining of electrons gives the atom a negative charge. The charge goes in the top right hand corner in a chemical symbol. Wave Functions Erwin Schrödinger: We can describe the electron mathematically, using quantum mechanics (wave mechanics). Schrödinger developed a wave equation to describe the hydrogen atom. An acceptable solution to Schrödinger’s wave equation is called a wave function. A wave function represents an energy state of the atom. The Wave Nature of Light Electromagnetic waves originate from the movement of electric charges. The movement produces fluctuations in electric and magnetic fields. Electromagnetic waves require no medium. Electromagnetic radiation is characterized by its wavelength , frequency , and amplitude . An Electromagnetic Wave The waves don’t “wiggle” as they propagate … … the amplitude of the “wiggle” simply indicates field strength . Wavelength and Frequency Wavelength (λ) is the distance between any two identical points in consecutive cycles. • Frequency (v) of a wave is the number of cycles of the wave that pass through a point in a unit of time. Unit = waves/s or s–1 (hertz ). Wavelength and Frequency The relationship between wavelength and frequency: c = λv where c is the speed of light (3.00 × 108 m/s) The Electromagnetic Spectrum UV, X rays are shorter wavelength, higher frequency radiation. Communications involve longer wavelength, lower frequency radiation. Visible light is only a tiny portion of the spectrum. A Continuous Spectrum White light from a lamp contains all wavelengths of visible light. When that light is passed through a prism, the different wavelengths are separated. We see a spectrum of all rainbow colors from red to violet – a continuous spectrum. A Line Spectrum Light from an electrical discharge through a gaseous element (e.g., neon light, hydrogen lamp) does not contain all wavelengths. The spectrum is discontinuous ; there are big gaps. We see a pattern of lines, multiple images of the slit. This pattern is called a line spectrum . (duh!) Line Spectra of Some Elements The line emission spectrum of an element is a “fingerprint” for that element, and can be used to identify the element! How might you tell if an ore sample contained mercury? Cadmium? Line spectra are a problem; they can’t be explained using classical physics … Planck … … proposed that atoms could absorb or emit electromagnetic energy only in discrete amounts . The smallest amount of energy, a quantum , is given by: E = hv where Planck’s constant, h, has a value of 6.626 × 10–34 J·s. Planck’s quantum hypothesis states that energy can be absorbed or emitted only as a quantum or as whole multiples of a quantum, thereby making variations of energy discontinuous. Changes in energy can occur only in discrete amounts. The Photoelectric Effect Light striking a photoemissive cathode causes ejection of electrons. Ejected electrons reach the anode, and the result is … … current flow through an external circuit. But not “any old” light will cause ejection of electrons … The Photoelectric Effect (cont’d) Each photoemissive material has a characteristic threshold frequency of light. When light that is above the threshold frequency strikes the photoemissive material, electrons are ejected and current flows. Light of low frequency does not cause current flow … at all. As with line spectra, the photoelectric effect cannot be explained by classical physics. The Photoelectric Effect Albert Einstein won the 1921 Nobel Prize in Physics for explaining the photoelectric effect. He applied Planck’s quantum theory: electromagnetic energy occurs in little “packets” he called photons . Energy of a photon (E) = hv • The photoelectric effect arises when photons of light striking a surface transfer their energy to surface electrons. • The energized electrons can overcome their attraction for the nucleus and escape from the surface … • … but an electron can escape only if the photon provides enough energy. The Photoelectric Effect Explained The electrons in a photoemissive material need a certain minimum energy to be ejected. Short wavelength (high frequency, high energy) photons have enough energy per photon to eject an electron. A long wavelength—low frequency—photon doesn’t have enough energy to eject an electron. The Bohr Model of Hydrogen When excited, the electron is in a higher energy level. Excitation: The atom absorbs energy that is exactly equal to the difference between two energy levels. Each circle represents an allowed energy level for the electron. The electron may be thought of as orbiting at a fixed distance from the nucleus. Emission: The atom gives off energy—as a photon. Upon emission, the electron drops to a lower energy level. Line Spectra Arise Because … Transition from n = 3 to n = 2. Transition from n = 4 to n = 2. … each electronic energy level in an atom is quantized. Since the levels are quantized, changes between levels must also be quantized. A specific change thus represents one specific energy, one specific frequency, and therefore one specific wavelength. Bohr’s Equation … … allows us to find the energy change (∆Elevel) that accompanies the transition of an electron from one energy level to another. Initial energy level: Final energy level: –B –B E i = —— n i2 E f = —— n f2 • To find the energy difference, just subtract: –B –B ∆Elevel = —— – —— = B n f2 n i2 1 1 ni nf — – — 2 2 • Together, all the photons having this energy (∆Elevel) produce one spectral line. Energy Levels and Spectral Lines for Hydrogen What is the (transition that produces the) longest-wavelength line in the Balmer series? In the Lyman series? In the Paschen series? De Broglie’s Equation Louis de Broglie’s hypothesis stated that an object in motion behaves as both particles and waves, just as light does. A particle with mass m moving at a speed v will have a wave nature consistent with a wavelength given by the equation: λ = h/mv This wave nature is of importance only at the microscopic level (tiny, tiny m). De Broglie’s prediction of matter waves led to the development of the electron microscope. De Broglie’s Equation… de Broglie just messed up the Bohr model of the atom. Bad: An electron can’t orbit at a “fixed distance” if the electron is a wave. An ocean wave doesn’t have an exact location—neither can an electron wave. Worse: We can’t even talk about “where the electron is” if the electron is a wave. Worst: The wavelength of a moving electron is roughly the size of an atom! How do we describe an electron that’s too big to be “in” the atom?? Wave Functions Erwin Schrödinger: We can describe the electron mathematically, using quantum mechanics (wave mechanics). Schrödinger developed a wave equation to describe the hydrogen atom. An acceptable solution to Schrödinger’s wave equation is called a wave function. A wave function represents an energy state of the atom. The Uncertainty Principle Werner Heisenberg: We can’t know exactly where a moving particle is AND exactly how fast it is moving at the same time. The photon that will enter the microscope, so that we might “see” the electron … … has enough momentum to deflect the electron. The act of measurement has interfered with the electron’s motion. The Uncertainty Principle A wave function doesn’t tell us where the electron is . The uncertainty principle tells us that we can’t know where the electron is. However, the square of a wave function gives the probability of finding an electron at a given location in an atom. Analogy: We can’t tell where a single leaf from a tree will fall. But (by viewing all the leaves under the tree) we can describe where a leaf is most likely to fall. Quantum Numbers and Atomic Orbitals The wave functions for the hydrogen atom contain three parameters called quantum numbers that must have specific integral values. A wave function with a given set of these three quantum numbers is called an atomic orbital . These orbitals allow us to visualize the region in which the electron “spends its time.” Quantum Numbers: n When values are assigned to the three quantum numbers, a specific atomic orbital has been defined. The principal quantum number (n) : • Is independent of the other two quantum numbers. • Can only be a positive integer (n = 1, 2, 3, 4, …) • The size of an orbital and its electron energy depend on the value of n. • Orbitals with the same value of n are said to be in the same principal shell. Quantum Numbers: l The orbital angular momentum quantum number (l) : Determines the shape of the orbital. Can have positive integral values from 0, 1, 2, … (n – 1) Orbitals having the same values of n and of l are said to be in the same subshell . Value of l 0 1 2 3 Subshell s p d f • Each orbital designation represents a different region of space and a different shape. Quantum Numbers: m l The magnetic quantum number (m l) : Determines the orientation in space of the orbitals of any given type in a subshell. Can be any integer from –l to +l The number of possible values for ml is (2l + 1), and this determines the number of orbitals in a subshell. Notice: one s orbital in each principal shell three p orbitals in the second shell (and in higher ones) five d orbitals in the third shell (and in higher ones) Electron Spin: m s • The electron spin quantum number (m s) explains some of the finer features of atomic emission spectra. • The number can have two values: +½ and –½. The spin refers to a magnetic field induced by the moving electric charge of the electron as it spins. The magnetic fields of two electrons with opposite spins cancel one another; there is no net magnetic field for the pair. The Periodic Table: A Preview A “periodic table” is an arrangement of elements in which the elements are separated into groups based on a set of repeating properties The periodic table allows you to easily compare the properties of one element to another The Periodic Table: A Preview Each horizontal row (there are 7 of them) is called a period Each vertical column is called a group, or family Elements in a group have similar chemical and physical properties Identified with a number and either an “A” or “B” More presented in Chapter 6 Concept Check Which photons have the highest energy? A) Cell phone operating at 1900 MHz B) A laser pointer using 635 nm light “Most Successful Theory of the 20th Century” Matter Dalton Thomson Rutherford Bohr & de Broglie Einstein Plank Maxwell Light Newton Heisenberg Schrödinger Wave Mechanics IV. Isotopes e.g. Determine the number of protons and neutrons in carbon-12, carbon-13, and carbon14. V. Masses of Atoms The mass of an atom is measured relative to the mass of a standard. The modern standard is carbon-12, which is assigned a mass of exactly 12 atomic mass units (amu). e.g. On this scale, a hydrogen atom has a mass of 1.008 amu. Note that 1 amu = 1.66054 x 10-24 g. Can we “see” the atoms? By Eyes By Optical microscope By Electron microscope no no possible Modern methods: The field emission microscope To visualize single atom or large molecules on the tip of fine metal points SEM(Scanning Electron Microscopy) To image the individual atoms in molecules and in crystals. TEM (Transmission Electron Microscopy) STM (Scanning Tunneling Microscopy) TEM STM image Atom manipulation By STM Fe atoms on Cu(111) Formation of Nuclides 1 1 H + 1 1 n → 1 0 2 1 1 0 H H is a proton and n is a neutron 2 H → 2 1 4 2 He