Chapter 1: The Electronic Structure of Atoms PDF

Chapter 1: The electronic structure of atoms Part 1 : structure of atoms See chapter 2 and 7 in the textbook 1  1. The Structure of the Atom-timeline...

Chapter 1: The electronic structure of atoms Part 1 : structure of atoms See chapter 2 and 7 in the textbook 1  1. The Structure of the Atom-timeline W. Heisenberg (1925) Democritus J. Dalton J.J Thomson E. Rhutherford N. Bohr (In the fifth century b.c.) (1808) (1897) (1911) (1913) E. Schrödinger J. Chadwik (1926) (1932) Matter consists of very Solid sphere Plum pudding Nuclear Planetary Quantum Model small, indivisible particles model model model model named atomos (meaning uncuttable or indivisible) 2  1. The Structure of the Atom The cathode ray tube : Discovery of the electron J.J Thomson (1897) Deflection plates Cathode ray 1) ΔV=0 Δx (-) 2) ΔV>> 0 1) ΔV=0 No deflection Deflection plates 2) ΔV>> 0 Deflection to the positive plate ΔV=voltage difference between two plates 3  1. The Structure of the Atom The cathode ray tube : Discovery of the electron by J.J Thomson (1897) Experiment interpretations and conclusions: Ray deflection toward the positive plate : the cathode ray is made of particles negatively charged Different metals give the same ray; the same particle is deflected Atoms have tiny negatively charged particles inside them called Electrons Electrons are negative The whole atoms are usually neutral It should be a positive charge in the atom that can balance the negatively charged electrons 4 1. The Structure of the Atom The cathode ray tube : Discovery of the electron Electron J.J Thomson (1897) Atom is not indivisible! Plum pudding model: The atom is a filled sphere formed of particles electrically positive and filled with negative electrons “like raisins in a cake” 5  1. The Structure of the Atom-timeline W. Heisenberg (1925) Democritus J. Dalton J.J Thomson E. Rhutherford N. Bohr (In the fifth century b.c.) (1808) (1897) (1911) (1913) E. Schrödinger J. Chadwik (1926) (1932) Matter consists of very Solid sphere Plum pudding Nuclear Planetary Quantum Model small, indivisible particles model model model model named atomos (meaning uncuttable or indivisible) 6  1. The Structure of the Atom The Nucleus : Rhutherford’s Atomic theory : nuclear model (1911) α-particles passed through Au-foil Deflected α-particles (See video) 7  1. The Structure of the Atom The Nucleus : Rhutherford’s Atomic theory : nuclear model (1911) alpha particles Plum pudding model Rhutherford’s model The interpretation : The gold (Au) atoms are mostly empty The majority of α-particles passes through the foil without hitting an obstacle Some α-particles were hitting a concentrated mass Rhutherford assumed that atom model is formed of empty space occupied by electrons centered with a positive mass called Nucleus. 8  1. The Structure of the Atom The Proton and the neutron The positively charged particles in the nucleus are called protons. Later experiments showed that there is a third type of subatomic particles, named neutrons. Strong interaction Neutrons are electrically neutral particles having a mass slightly greater than that of protons. There are other subatomic particles (quarks), but the electron, the proton, and the neutron are the three fundamental components of the atom that are important in chemistry. 9 1. The Structure of the Atom 10  1. The Structure of the Atom-timeline W. Heisenberg (1925) Democritus J. Dalton J.J Thomson E. Rhutherford N. Bohr (In the fifth century b.c.) (1808) (1897) (1911) (1913) E. Schrödinger J. Chadwik (1926) (1932) Matter consists of very Solid sphere Plum pudding Nuclear Planetary Quantum Model small, indivisible particles model model model model named atomos (meaning uncuttable or indivisible) 11  1. The Structure of the Atom Bohr’s Atomic theory (1913) Bohr’s model supposed that an atom is a small, positively charged nucleus surrounded by electrons that travel in circular orbits around the positively charged nucleus. Every circular orbit will have a certain amount of fixed energy and these circular orbits were termed orbital shells The different energy levels or oribits are denoted by integers such as n=1 or n=2 or n=3, etc or K, L, M, etc 12  1. The Structure of the Atom-timeline W. Heisenberg (1925) Democritus J. Dalton J.J Thomson E. Rhutherford N. Bohr (In the fifth century b.c.) (1808) (1897) (1911) (1913) E. Schrödinger J. Chadwik (1926) (1932) Matter consists of very Solid sphere Plum pudding Nuclear Planetary Quantum Model small, indivisible particles model model model model named atomos (meaning uncuttable or indivisible) 13  1. The Structure of the Atom Schrödinger Atomic theory (1926) -Schrödinger stated that electrons do not move in set of paths around the nucleus(orbits), but in waves and occupy many positions where the shape of these electron cloud is called Orbitals. -It is impossible to know the exact location of electrons, instead we have clouds of probability called orbitals in which we are more likely to find an electron. -This atomic model is known as the quantum mechanical model of the atom. 14 2. Atomic Number, Mass Number, and Isotopes Atomic Number, Mass Number All atoms can be identified by the number of protons and neutrons they contain. The atomic number (Z) is the number of protons (Np) in the nucleus of each atom of an element. The mass number (A) is the total number of neutrons (Nn) and protons (Np) present in the nucleus of an atom of an element. In a neutral atom: Np = Ne (Ne : number of electrons) Z= Np = Ne (neutral atom) A = Np + Nn 12 Nn = A - Z Example : 5𝐵 A= 12 ; Z= 5; Nn= 7 15 2. Atomic Number, Mass Number, and Isotopes Isotopes Isotopes are atoms that have the same atomic number Z but different mass numbers A. Most elements have two or more isotopes. For example, there are three isotopes of hydrogen: 16 Application 1 Solution : Z= Np = Ne (neutral atom) A = Np + Nn Nn = A - Z Np Nn Ne 20 11 9 11 11𝑁𝑎 22 11𝑁𝑎 11 11 11 17 8 9 8 𝑂 Carbon-14 6 8 6 17  From Classical Physics to Quantum Mechanics Theory States are measured continuously States are quantized to discrete values Classical mechanics treat particles and waves differently while in quantum mechanics, every object has a particle and wave nature associated with it. Radiation and matter display both wavelength and particle like properties 18  3. The wave-particle duality of light 1. Light as a wave : double-slit 1. Light as a particle: the experiment photoelectric effect experiment 19 3.1. Light waves Properties of waves review Waves have a periodic variation of some quantity Examples : water, sound, light waves, etc Water level Ocean water waves Wavelength λ (lambda) is the distance between identical points on successive waves. Units: The frequency ν (nu) is the number of waves that pass through a particular point in 1 second. λ (nm, cm or m) Amplitude is the vertical distance from the midline of a wave to the peak. ν (Hz or counts/s) 20  3.2. Light waves Light = Electromagnetic Radiation An electromagnetic wave has an electric field component and a magnetic field component. Electromagnetic Radiation has a constant speed : The speed of light : C = λ. ν (3) C is the speed of electromagnetic waves, estimated to 2.9979 x 10 8 meters per second in vacuum λ : the wavelength (m) ν: the frequency in Hz Double slit experiments shows that light behaves like a wave (See video) 21 Types of electromagnetic radiations 22  Application 2 Two electromagnetic waves are represented below a) Which wave has higher frequency? b) If one wave represents visible light and the other represent infrared radition, which wave is which? Solution: (a) Based on this equation (ν = C/λ), the longer the wavelength, the lower the frequency. So, the wave on the top has a shorter wavelegth so higher frequency. (b) The electromagnetic spectrum indicates that infrared radiation has longer wavelength than visible light. Therefore, the wave on the bottom would be the infrared radiation. 23 Application 3 What is the wavelength of a wave having a frequency of 3.76 x 1014 s-1 Solution : C=λ.ν 𝑪 2.9979 x 108(m/s) λ= = = 7.97x 10-7 m ν 3.76 x 1014(counts/s) 24  3.2-Light as a particle : the photoelectric effect experiment ν < ν0 ν > ν0 Case 2: A beam of UV light is hitting a Case 1 : A beam of visible light metal surface can eject electrons. is hitting a metal surface. e- KE metal ν : is the frequency of incident radiation ν0 : is the smallest frequency required to eject an electron from the metal KE: kinetic energy of the ejected electron Case 1 ν < ν0 No electron is ejected Case 2 ν > ν0 Electrons will be ejected and they will also acquire some kinetic energy (KE). ν = ν0 Light will have just enough energy to knock the electrons 25 3.2-Light as a particle : the photoelectric effect experiment 4 additional experiments to explain the property of light as a particle. 1 Nb of e- 2 KE of e- ν0 ν of light ν0ν of light At constant intensity, the frequency of light has Plot of the KE of ejected electrons as a function of no effect on the number of electrons (Nb of e-) frequency of incoming light at constant intensity, 4 3 KE of e- Nb of e- Intensity I of light Intensity I of light Plotting the KE of ejected electrons as a function of Plotting the Nb of ejected electrons as a function of the intensity of incoming light at constant ν. the intensity of incoming light at constant ν. 26  We conclude from the previous experiments that: At constant intensity, increasing the frequency of the incident light does not affect the number of ejected electrons (Nb of e-) but increases their kinetic energy. At constant frequency (the same electromagnetic radiation of incident light), increasing the intensity of the light does not affect the kinetic energy of the emitted electrons but increases their number. The photoelectric effect could not be explained by the wave theory of light. 27 3.2-Light as a particle : the photoelectric effect experiment Max Planck quantum theory gave the name quantum to the smallest quantity of energy that can be emitted (or absorbed) in the form of electromagnetic radiation. Albert Einstein was based on Max Planck quantum theory when he tried to solve the photoelectric effect enigma and suggested that a beam of light is really a stream of particles called photons. According to Einstein, each photon possesses an energy given by this equation : Where ν is the frequency of light and h is Planck’s constant light behaves either as a wave or as a stream of particles. This concept, called particle-wave duality 28  3.2-Light as a particle : the photoelectric effect experiment Plot of Kinetic energy (KE) as a function of frequency ν for several metals (M) M1 M2 Kinetic energy (KE) of M3 All metals exhibit the same slope (a) (linear curves are parallel) ejected electron KE= a ν + b a=6.626x10-34 Js ν0(M1) ν0(M2) ν0(M3) ν of light a= Planck’s constant -hν0(M1) Planck’s constant = h = 6.626x10-34 Js -hν0(M2) b=intercept= -h ν0 -hν0(M3) KE=hν KE= hν––hν hν00 hν==KE hν KE++hν hν00 or where ν frequency of incident light, hν the energy of incident light , ν0 threshold frequency, hν0 threshold energy also called work function, W, which is a measure of how strongly the electrons are held in the metal. KE is the kinetic energy of the ejected electron. 29 A metal ejects from its surface a number of electrons that is proportional to the number of photons the metal absorbs. e e Photons striking the metal Electrons ejected from the metal have each an energy E=hν e have KE= hν-W e e Metal W= hν0 Thus, the intensity of the light is propotional to the number of photons absorbed 30 Application Consider the work function of a metal equal to 1.55 eV and an incident UV light of wavelength 430 nm. Calculate the maximum kinetic energy of the photoelectrons. Solution: KE= hν – hν0 E=h.ν = h.C/ λ C=λ.ν 6.626x10−34 (Js) 2.9979 x 10 8 (m/s) 𝐸= = 4.626 x 10−19 J 430𝑥10−9 (𝑚) KE= 4.626 x 10−19 -(1.55x1.6x10-19)=2.15x10-19 J 1nm = 𝟏𝟎−𝟗 m 1 eV= 1.6x10-19 J 31 4. Bohr’s Theory of the Hydrogen Atom Generalities : emission spectra types Einstein's contributions were very useful to solve another physics "mystery" from the nineteenth century that was : the emission spectra of atoms. Further measurements realized on the interaction of light with matter that has been put under different sources of energy like thermal energy, high voltage or electric discharge, revealed that the emission spectra can be either continuous or line spectra of radiation. tungsten lightbulb Glowing hot iron bar line spectra of radiation emitted by hydrogen (continuous emission) (continuous emission) 32  Emission Spectrum of various elements: Every element has a unique set of absorption and emission lines. Elements can be identified from their emission or absorption spectra. The pattern of lines is known as a spectral signature 33 4. Bohr’s Theory of the Hydrogen Atom Bohr postulated that the electron is allowed to occupy only certain circular trajectories called orbits (like sun and planets) of specific energies Bohr attributed the emission of radiation of energized hydrogen atom to the electron droping from higher energy allowed orbit to a lower one by emissting a photon Bohr showed that the energies that an electron in hydrogen atom can occupy are given by : where RH , the Rydberg constant for the hydrogen atom, has the value 2.18 x 10 -18 J= 13.6 eV. The number n is an integer called the principal quantum number; it has the values n =1, 2, 3, etc 34  Hydrogen Atom energy levels En Free electron n=∞ 0 -RH/4²= -0.136 x 10-18 J n=4 -RH/3²= -0.242 x 10-18 J n=3 En is called binding energy (of hydrogen atom) Note all binding energies are negative -RH/2²= -0.545 x 10-18 J n=2 -RH/1²= -2.18 x 10-18 J n=1 Ground state Most statbe state Lowest energy 35  Hydrogen Atom energy levels En n=∞ 0 -RH/4²= -0.136 x 10-18 J n=4 -RH/3²= -0.242 x 10-18 J n=3 -RH/2²= -0.545 x 10-18 J n=2 -RH/1²= -2.18 x 10-18 J n=1 36 4. Bohr’s Theory of the Hydrogen Atom When an atom absorbs energy, it causes that the electron moves from a lower-energy state (characterized by a smaller n value) to a higher-energy state (characterized by a larger n value) Emission energy (in the form of a photon) occurs when the electron moves from a higher-energy state to a lower-energy state The difference between the energies of the initial and final states is : Δ𝐸 = 𝐸𝑛𝑓 − 𝐸𝑛𝑖 1 𝐸𝑛𝑓 = −𝑅𝐻 ( 2 ) 𝑛𝑓 1 𝐸𝑛𝑖 = −𝑅𝐻 ( 2 ) 𝑛𝑖 −𝑅𝐻 −𝑅𝐻 1 1 Δ𝐸 = 𝐸𝑛𝑓 − 𝐸𝑛𝑖 = 2 − = 𝑅𝐻 ( − ) 𝑛𝑓 𝑛𝑖2 𝑛𝑖 2 𝑛𝑓 2 1 1 𝛥𝐸 = 𝑅𝐻 ( 2 − 2 ) 𝑛𝑖 𝑛𝑓 37 Summary absorption & emission processes nf ni ni nf 1 1 𝛥𝐸 = 𝑅𝐻 ( 2 − 2 ) ν should be always positive! 𝑛𝑖 𝑛𝑓 𝑅𝐻 1 1 𝜈= ( − ) 𝜟𝑬 < 0 (ni>nf) indicates that this energy is associated with an emission process ℎ 𝑛𝑓 2 𝑛𝑖 2 𝜟𝑬 > 0 (ni