Chapter 7 Beyond Rutherford to The Most Successful

Chapter 7 Beyond Rutherford to “The Most Successful Theory of the 20 th Century”

View Rutherford’s experiment http: //www. learnerstv. com/animati on/chemistry/ruther 14. swf

Rutherford’s Atomic Model (“planetary model”) Empty space e- Orbiting electron (fixed radius) Nucleus Diameter = 10 -15 m Diameter of atom = 10 -10 m

Problem with Rutherford’s Model !! n It did not obey the classical laws of physics According to Newton’s classical laws, electrons orbiting the nucleus should radiate energy, slow down, and be pulled into the nucleus & collapse the atom But atoms don’t collapse, yet Rutherford’s experiment showed that electrons can be located a distance away from the nucleus. n So, the model of the _______ behavior is flawed. n

Collision of Ideas Matter Dalton Thomson Rutherford Bohr & de Broglie Einstein Plank Maxwell Light Newton ?

What is the nature of light?

By the 17 th century, light was found to n travel in straight lines n reflect & refract n transmit energy from one place to another Isaac Newton: “Light is a particle” Newton’s prism

The WAVE THEORY, advocated by Robert Hooke Christian Huygens argued that light is a wave. The PARTICLE THEORY, advocated by Isaac Newton and Pierre Laplace, argued that light was made up of a stream of tiny particles (“corpuscles”).

Two Competing Theories n. The theory of light

infrared ultraviolet “white light” light energy composed of a continuous spectrum of visible electromagnetic radiation

Basics of wave theory Wavelength = distance between wave crests (m) Frequency = cycles per second (Hz)

Electromagnetic Wave Theory (1865) · Based on experiments of Michael Faraday · Theory developed by James Clerk Maxwell Electromagnetic waves have a variety of wavelengths, but all travel at the speed of light, c = 2. 998 × 108 m/s Based on conservation of energy, Maxwell derived the wave equation, c=

Electromagnetic Spectrum 1020 Hz 10 -6 nm higher energy 1014 Hz 1010 Hz 108 nm lower energy

ROY G BIV low energy high energy Colors in the visible spectrum: Red, Orange, Yellow, Green, Blue, Indigo & Violet

Problems with the Wave Theory of Light By the mid-1800 s, the wave theory became predominant, but…… When light interacted with matter, the wave theory failed. The important examples are: 1. Blackbody Radiation 2. The Photoelectric Effect 3. Emission Spectra of Atoms

Problem #1. Blackbody Radiation blackbody “object that absorbs all the colors in the spectrum” Blackbody Simulation actual spectrum When heated to a high enough temperature, the blackbody radiates white light. The wave theory predicts a continuous spectrum of emitted light, but theory fails to match experiment.

Planck’s Quantum Theory n Measured blackbody radiation did not produce a continuous spectrum, as wave theory predicted n In 1900, German Physicist Max Planck proposed a new quantum theory of light: Light is taken up and given off by a blackbody not as a continuous wave, but in little “packets” of light energy of specific values Planck called these packets “quanta” (singular is quantum) of energy

Quantum Theory of Light and Quantum Physics n Plank’s quantum theory of light was a historical turning point in physics, transitioning classical physics from the 18 th and 19 th centuries to the quantum physics of the 20 th century.

Problem #2 Photoelectric Effect Animation

Problem #2. Photoelectric Effect n Imagine shining light of various wavelengths (energies) on the surfaces of different metals Animation n Only light energies above a certain threshold cause electrons to be ejected from the metal surface n This conflicts with predictions of the wave theory

Einstein’s Photons In 1905, a Swiss patent clerk proposed that light consists of particles called photons. n As Planck proposed, Einstein’s photons have a certain quanta of energy (based on wavelength) n His model of light solved the problem of the photoelectric effect. Duality of Light n n Wave behavior n Particle behavior

Solar Sail (based on Einstein’s photon theory) - Light reflecting off a mirror imparts momentum - Yet light has no mass (experiment by Compton in 1923) Cosmos 1 concept

Energy of Photons n At a specific frequency (or wavelength) photons possess a specific quantity of energy (E ) E = h n E = h c/ Planck’s constant h = 6. 626 x 10 -34 J·s Question: Is 400 nm light (violet light) more or less energetic than 750 nm light (red light)?

Concept Check The energy required to dislodge electrons from sodium metal via the photoelectric effect is 275 k. J/mol. What wavelength (in nm) has sufficient energy per photon to dislodge an electron from the surface of sodium? sodium

Concept Check Which photons have the highest energy? A) Cell phone operating at 1900 MHz B) A laser pointer using 635 nm light

Problem #3. Atomic Line Spectra Flame tests http: //college. cengage. com/chemistry/ general/ebbing/general_chem/9 e/assets/ instructors/protected/videos. html#Chapter 7 n. Periodic Table of Line Spectra

Problem #3. Atomic Line Spectra Emission spectra for pure elements n Periodic Table of Line Spectra Fireworks

Niels Bohr (1885 -1962) n Danish physicist who worked with J. J. Thomson at Cambridge University in 1911. He didn’t agree with Thomson’s atomic model, so worked for Rutherford in 1912. n In 1912, in a bold step, he suggested that the classical laws of physics cannot be applied to matter as small as atoms and electrons. Instead, new laws are needed n Bohr sought to solve the problem with Rutherford’s atomic model and explain the phenomenon of atomic spectra, by applying the quantum theory of light to atoms and electrons

Bohr’s Quantum Atomic Model n Postulated that the energy of the electron must be quantized. Only certain electron energies are possible. n Orbit radii (energy levels) correspond to definite energies n Energy is emitted or absorbed by the electron only as the electron changes from one allowed energy level to another n = energy level number or principal quantum number Why does an electron possess energy? 1) 2)

Stairstep How do quantized energy levels explain spectral lines? analogy n Atoms “place” electrons in lowest possible energy levels (“ground state”) n When electrons are provided with enough energy, they “jump” to higher energy levels, where they are unstable (“excited state”) n The electrons then fall back down to the lower possible energy levels, releasing absorbed energy as a photon of light n We see these photons as the spectral lines emitted by excited atoms Energy of H electron = E = -RH/n 2 n = 1, 2, 3, … ∞ RH = 2. 179 x 10 -18 J

energy levels

H emission spectrum “quantum jump” ∆E 4→ 2 = E 2 - E 4 = h 4→ 2

A “quantum jump” Emission ∆E = E 2 - E 4 = h 4→ 2 Absorption ∆E = E 4 – E 2 = h 2→ 4

Simulations of Bohr Model n Visible emission spectral lines of hydrogen

Success & Limitation of Bohr’s Quantum Model n Explained the existence of spectral lines n Solved the problem with Rutherford’s model of the hydrogen atom n But, the mathematics only worked for atoms with 1 electron! How can this model be made to work for all elements?

de Broglie’s Novel Notion 1923 Light was “known” (thought) to be a wave, but Einstein showed that it also acts particle-like. Electrons were “known” to be particles mass & charge. French physicist: What if …… electrons behaved as waves also Diffraction pattern obtained by firing a beam of electrons through a crystal.

Dr. Quantum video

Werner Heisenberg The Uncertainty Principle speed position n In 1927, German physicist, proposed that the dual nature of the electron places limitations on how precisely we can know both the location and speed of the electron n Instead, we can only describe electron behavior in terms of probability

Heisenberg’s Uncertainty Principle Wave behavior limits what can be known! (±x)(±vx) ± position h 4 m ± speed n What if the particle has a small mass? n What if the electron’s position is known very precisely? n What if the electron’s speed is known very precisely? Can the electron’s orbit be precisely defined?

Erwin Schrodinger Wave Equation & Wave Mechanics n In 1926, Austrian physicist, proposed an equation that incorporates both the wave and particle behavior of the electron n When applied to hydrogen’s 1 electron atom, solutions provide the most probable location of finding the electron in the first energy level n Can be applied to more complex atoms too!

Electron Characteristics • Extremely small mass • Located outside the nucleus • Moving at very high speeds • Have specific energy levels • Standing wave behavior

Baseball v. Electron A baseball behaves as a particle and follows a predictable path. BUT An electron behaves as a wave, and its path cannot be predicted. All we can do is to calculate the probability of the electron following a specific path.

What if a baseball behaved like an electron? = h /(mu) mass speed Characteristic wavelength ( ) • baseball 10 -34 m • electron 0. 1 nm So, all we can predict is…. .

“deterministic” “probabilistic”

Bohr Model v. Quantum Mechanics Bohr Energy Electron Position/Path Elements Quantum Mechanics

Quantum Mechanics Model The electron's movement cannot be known precisely. We can only map the probability of finding the electron at various locations outside the nucleus. The probability map is called an orbital. The orbital is calculated to confine 99% of electron’s range. Energy of the electron is quantized into sublevels.

Quantum Mechanics Model Describes the energy, arrangement and space occupied by electrons in atoms Electron’s energy is quantized Quantum Mechanics Mathematics of waves to define orbitals (wave mechanics)

“Most Successful Theory of the 20 th Century” Matter Dalton Thomson Rutherford Bohr & de Broglie Einstein Plank Maxwell Light Newton m u t n a u Q s c i n a h c Me Heisenberg Schrödinger Wave Mechanics