CHAPTER 6 The Structure of Atoms Chapter Outline 6-1 Electromagnetic Radiation 6-2 Quantization: Planck, Einstein, Energy and Photons 6-3 Atomic Line Spectra and Niels Bohr 6-4 Particle-Wave Duality: Prelude to Quantum Mechanics 6-5 The Modern View of Electronic Structure: Wave or Quantum Mechanics 6-6 The Shapes of Orbitals 6-7 One More Electron Property: Electron Spin Atomic Structure A model describing the structure of an atom. When Atoms react It is the ELECTRONS that react Much of our understanding of ELECTRONS comes from Analysis of the Absorption or Emission of Light Electromagnetic Radiation Atoms gain energy and they become excited Added energy is absorbed by electrons and then released in the form of “Electromagnetic Radiation” Outer atom is almost vacuum Electromagnetic Radiation energy traveling through space particles or waves? More on this later c = c = speed of light 2.998 × 108 ms−1 = wavelength lambda typically nm = frequency nu s−1 or a hertz Electromagnetic Radiation Consists of oscillating electric and magnetic fields traveling through space Travel at the same rate-----speed of light in a vacuum Typical units c = 3.00 108 m/s c = 3.00 108 ms−1 = s−1 or cycle/s or Hertz (Hz) = distance radio waves - m visible light - nm (10−9 m) Electromagnetic Radiation Electromagnetic Radiation or “Light” is composed of two orthogonal vectors: An electric wave and a magnetic wave. Electromagnetic Radiation wavelength Amplitude wavelength Node Ultraviolet radiation Red is lowest The intensity of light is a function of the wave’s amplitude. A point of zero amplitude is called a “node”. Electromagnetic Radiation Light is characterized by its wavelength and frequency. Electromagnetic Radiation Cell phone’s radiation is between Microwave and Radio waves Dangerous light is started by UV. Till rainbow region to long radio waves is safe. The visible region of the electromagnetic spectrum is only a small portion of the entire spectrum. Niels Bohr/Max Planck Discovered Quanta If you were told that you could drive your car at 23.4 mph or 28.9 mph or 34.2 mph, but never any speed between in between these values…..you wouldn’t believe it!! Yet they discovered this about electrons in atoms. What are Quanta? In 1900 the German physicist Max Planck proposed that light, heat, and other forms of radiation come in tiny bundles, which he called quanta. The amount of energy in a single particle, he said, depended on the frequency and can be given by the following equation: E=h where is the frequency of the wave and h is a constant that came to be called Planck's constant. Quantization of Energy Max Planck (1858-1947) proposed that light waves existed as discrete packets of energy, “quanta” in order to account for the prediction that an ideal black body at thermal equilibrium will emit radiation with infinite power. According to classical physics, the intensity of emitted light approaches infinity as the wavelength of the light approaches zero. Quantization Packet of energy Planck (1900); 1918 Nobel Prize Energy = hv Energy is restricted h = 6.63 10−34 J s E = h, E = 2h, E = 3h, … Energy is quantized Since h is small, macroscopic level energy appears to be continuous. Quantization of Energy An object can gain or lose energy by absorbing or emitting radiant energy in QUANTA. A quanta of energy is the smallest unit of energy that may be exchanged between oscillators or emitted as radiation. It is too small to be observed in the classical world in which we live. Energy of radiation is proportional to frequency Energy = h · v h = Planck’s constant = 6.6262 × 10−34 J·s Planck’s Law E = hν yields: E and c hxc • As the frequency of light increases, the energy of the photon increases. • As the wavelength of light increases, the energy of the photon decreases. Blue Light, (higher frequency) has more energy than Red Light, with a lower frequency. Real World Similar to Rungs on a ladder Or Notes on a piano Flip books Photoelectric Effect Photoelectric Effects Certain metals will release (eject) electrons when light strikes the metal surface. The energy of the light must exceed a minimum or “threshold energy” for this to occur. Any excess energy beyond this minimum goes into the kinetic energy of the ejected electron. (They fly away with greater velocity). Photoelectric Effect Classical theory suggests that energy of an ejected electron should increase with an increase in light intensity. This however is not experimentally observed! No ejected electrons were observed until light of a certain minimum energy is applied. Number of electrons ejected depends on light intensity so long as the light is above a minimum energy. (This “minimum energy” is also the ionization energy of the metal.) Photoelectric Effect Conclusion: There is a one-to-one correspondence between ejected electrons and light waves. This can only occur if light consists of individual units called “PHOTONS” . A Photon is a packet of light of discrete energy. The Gist of the Photoelectric Effect Demonstrated that light, usually considered to be a wave, can also have the properties of particles, albeit WITHOUT MASS More on Photoelectric For each metal there is a threshold wavelength On Periodic Table Cesium can emit electrons with red ㄴGroup 1 light, some other metals require yellow light or even ultraviolet to emit Intensity vs. Energy Why not just shine a “bright light?” Carnival game analogy - knock down the bottles which would you choose? A B 50 nerf balls 1 baseball 50 nerf balls - more intense 1 baseball - more energy Photoelectric Effect Evidence for Quanta Einstein (1905); 1921 Nobel Prize Video game analogy nickels and dimes, no matter how many, will not get a video game to work 1 quarter is required Line Spectra Gases are “excited” electrons have more energy than normal as electrons go from higher to lower energy, light is emitted Line Emission Spectra of Excited Atoms Excited atoms emit light of only certain wavelengths. The wavelengths of emitted light are unique to each individual element. Atomic Spectra and Bohr One view of atomic structure in early 20th century was that an electron (e-) traveled about the nucleus in an orbit. 1. Any orbit should be possible and so is any energy. 2. But a charged particle moving in an electric field should emit energy. End result should be destruction! Atomic Spectra and Bohr Model Bohr asserted that line spectra of elements indicated that the electrons were confined to specific energy states called orbits. The orbits or energy levels are “quantized” such that only certain levels are allowed. + n = 1, 2, 3... The Bohr Model: r n = n 2ao ao = Bohr radius (53 pm) Atomic Spectra and Bohr Model Bohr asserted that line spectra of elements indicated that the electrons were confined to specific energy states called orbits. + The lines (colors) corresponded to “jumps” or transitions between the levels. Atomic Spectra and Bohr Bohr said classical view is wrong. Need a new theory — now called QUANTUM or WAVE MECHANICS. e- can only exist in certain discrete orbits — called stationary states. e- is restricted to QUANTIZED energy states. Energy of state = − c/n2 where n = quantum no. = 1, 2, 3, 4, .... Atomic Line Spectra and Niels Bohr Line Spectra of H, Hg, and Ne Line Spectrum of Hydrogen Balmer series - empirical 30 years before it was explained Bohr Model E is negative (–) for all values of n lower (more –) values — more stable lowest for n = 1 — most stable zero (0) for n = Line Spectrum of Hydrogen Electron is very stable = 1 Energy Transitions ground state - lowest energy level (n=1) excited state - higher energy level than the ground state (n>1) E = 0; electron completely separated from H nucleus (n = ) The Balmer Equation Mathematical relationship among observed frequencies. An equation was found that could calculate the wavelength of the red, green, an blue lines in the visible emission spectrum of HYDROGEN. Calculating E E = Efinal – Einitial v equals the wave number not frequency 1 1 1 Rh 2 2 2 n2 When n >2 Knowing that R = Rydberg constant = 1.0974 × 107 m−1 Excited State Energy Absorption Bohr Model - Summary Successes - describes the line spectra of the hydrogen atom Limitations - only works for 1-electron systems (H, He+) Bohr - 1929 Nobel Prize “If light can be viewed in terms of both wave and particle properties, why cant particles of matter, such as electrons, be treated the same way?” Yes. But it’s so small. You cannot see. DeBroglie Matter has wave properties h mv 1 J = 1 kgm2 s−2 h = 6.63 × 10−34 J s Planck’s constant m = mass v = velocity DeBroglie Matter has wave properties not observable for big pieces of matter, such as golf balls observable for small pieces of matter such as electrons Wavelength of a Golf Ball 82.5 g, v = 255 km/hr (150 mph) = 1.13 × 10−34 m big particle; very short wavelength Wavelength of an Electron 9.11 × 10−28 g, v = 3.00 × 107 m/s = 2.43 × 10−11 m small particle, longer wavelength Wave or Quantum Mechanics Taking on the ideas of Bohr, de Broglie and Heisenberg, Irwin Schrödinger proposed that matter can be described as a wave. In this theory, the electron is treated as both a wave and a particle. An electron is described by a Wave Function “” that completely defines a system of matter. Quantum Mechanics e– has only certain allowed energies results presented from mathematical relationship of Schroedinger (Nobel Prize, 1932) wave function — no physical meaning 2 — probability of finding an electron in a region in space (orbital) Always ends at 0 Wave motion: wave length and nodes “Quantization” in a standing wave From the book in search of Shrodinger’s cat If it were ever possible to know the position and velocity of every particle in the universe, then it would be possible to predict with utter precision the future of every particle and therefore the future of the universe. Uncertainty principle Heisenberg (1932 Nobel Prize) for an electron, cannot know simultaneously both position momentum observation affects behavior mouse - flashlight analogy stick in stream analogy Types of Orbitals • The solutions to the Schrödinger equation yields the probability in 3-dimensons for the likelihood of finding an electron about the nucleus. • It is these probability functions that give rise to the familiar hydrogen-like orbitals that electrons occupy. Every orbital’s maximum electron is 2 Quantum Numbers & Electron Orbitals Quantum Numbers are terms that arise from the mathematics of the Schrödinger equation. They describe location of an electron in a particular orbital much like an address. Each electron in an orbital has its own set of three quantum numbers. “n”= 1, 2, 3, 4…up to infinity Principal Quantum Number shell Azimuthal or Angular Quantum Number “l” = 0, 1, 2, 3…up to a maximum of “n – 1” sub-shell Magnetic Quantum Number “ml” ml may take on the value an integer from – l to + l individual orbitals Quantum Numbers & Electron Orbitals n defines the Principal energy level “shell” There are n “sub–shells” for each n – 1 level corresponding to l if “n” equals: n=1 n=2 n=3 “l” can have values of: l=0 l=0&1 l = 0, 1 & 2 Each l is divided into (2l + 1) ml “orbitals” separated by orientation. if “l” equals: “ml” can have values of: l=0 ml = 0 l=1 ml = 0, ±1 l=2 ml = 0, ±1, ±2 Quantum Numbers & Electron Orbitals Each “l” within an “n-level” represents a sub-shell. Each “l” sub-shell is divided into ml degenerate orbitals, where ml designates the spatial orientation of each orbital. l=0 l=1 l=2 l=3 Type of orbital “s” sub-shell (sharp) “p” sub-shell (Principal) “d” sub-shell (diffuse) “f” sub-shell (fine) # of orbitals 1 3 5 7 each subshell contains 2l+1 orbitals Orbitals The region in which an electron can be found within an atom Orbitals and Quantum Numbers Orbitals have a characteristic size and shape n = principal QN; energy and size l = angular momentum or azimuthal QN; shape ml = magnetic QN; orientation orbitals with same n in same shell orbitals with same n & l in same subshell QN Summary: n, l, ml describe an orbital ms describes spin of e– in an orbital a set of 4 QN describes an e– like an address describes a location no two e– in an atom can have identical sets of 4 QN’s Pauli Exclusion Principle Summary of Quantum Numbers Allowed Quantum Numbers n = 1,2,3, …. l = 0,1,2, ….(n-1) l = 0, s l = 1, p l = 2, d l = 3, f ml = (-l …., 0, …. +l) Types of Orbitals s orbital p orbital d orbital s-Orbitals l = 0, ml = 0 2l+1 = 1 one s-orbital that extends in a radial manner from the nucleus forming a spherical shape. p-Orbitals The three degenerate p-orbitals spread out on the x, y & z axis, 90° apart in space. d-Orbitals s-orbitals have no nodal planes (l = 0) p-orbitals have one nodal plane (l = 1) d-orbitals therefore have two nodal planes (l = 2) Arrangement of Electrons in Atoms Each orbital can accommodate no more than 2 electrons Since each electron is unique, we need a way to distinguish the individual electrons in an orbital from one another. This is done via the 4th quantum number, “ms”. Stern-Gerlach Experiment (1922) If atoms with a single unpaired electron are placed in a magnetic field, they showed there are two orientations for the atoms. The electron spin was aligned with the field or opposed to the field. Electron Spin Since there were 2 pathways in the Stern-Gerlach experiment, there must be 2 spins affected by the magnetic field. One spinning to the right, one spinning to the left. Each “spin state” is assigned a quantum number ms = ± ½ + ½ for “spin up” ½ for “spin down” Electron Spin Electron Spin Quantum Number, ms The experiment results indicate that electron has an intrinsic property referred to as “spin.” Two spin directions are given by ms where ms = +1/2 and -1/2. Electron Spin It is not that the electrons are actually spinning on axis... Rather it is that the mathematics that describe the electrons “looks” like they are spinning on axis. ms, e– spin ms, spin quantum number, indicates spin ms = +½ ms = –½ Magnetic Properties of Atoms and Ions Paired electrons – diamagnetic Ferromagnetic- metals with magnetic properties Unpaired electrons - paramagnetic attracted by a magnetic field attraction proportional to number of unpaired e– Electron Spin and Magnetism • Diamagnetic Substances: Are NOT attracted to a magnetic field • Paramagnetic Substances: ARE attracted to a magnetic field. • Substances with unpaired electrons are paramagnetic.