Quantum Theory, Part 2

1. Quantum Theory, Part 2 The Atom Is it a particle or a wave? Day 1

2. Is it a particle or a wave? Falling Ball Ground level • Particle • Defined location at a particular time • Can be at rest, moving, or accelerating

3. Is it a particle or a wave? • Wave • Need to see crests and troughs to define them. • Waves are oscillations in space and time. Direction of travel, velocity Up-down oscillations Wavelength, frequency, velocity and oscillation size defines waves

4. Basic difference in behaviour? When particles collide, they cannot pass through each other. They can bounce or they can shatter! Before collision After collision Before collision Another after collision state shatter

5. Watch the collision between a truck with ladder on top and a car at rest ! Note the ladder continue its motion forward …..

6. Head on collision of a car and truck Collision is inelastic – the small car is pushed along by the truck……

7. The basic difference between Waves and Particles: - Waves can pass through each other! - As they pass through, they can enhance or cancel each other. -Afterwards, they regain their original form

8. Waves and Particles: Spread in space and time Waves Can be superposed – show interferenceeffects Pass through each other Localized in space and time Particles Cannot pass through each other - they bounce or shatter.

9. What is Light?!?!? • Planck’s Experiment • Einstein’s Experiment PARTICLE! Blackbody Radiation – energy is quantized PARTICLE! Photoelectric Effect – light is made up of photons.

10. Laser

11. If light is a particle then….

12. Thomas Young • Performed the Double Slit Experiment to test the wave nature of light.

13. Wave Properties

15. INTERFERENCE (2D) + = Constructive Interference = more intense (brighter) wave (AMPLIFIED) + = Destructive Interference = no amplitude (Node) meaning no wave (CANCELED)

17. A prism bends light. Different Colors are bent by different amounts. White Light

22. Two source interference constructive interference ------- destructive interference -------

23. Two source interference – S1P S2P Path difference = = 1 wavelength constructive interference ------- destructive interference ------- =  P S2 S1

24. Two source interference Path difference for constructive interference = n  (where n is an integer) 0  2 3 constructive interference ------- destructive interference -------

25. Two source interference (n + ½) Path difference for destructive interference = (where n is an integer) ½ 1½  2½  constructive interference ------- destructive interference -------

26. Interference in the Experiment

27. Young’s Double Slit Experiment

28. CONCLUSION: Light is a wave!

29. Oui, Oui, monami Well along came Louis de Broglie and he said if light can travel in wavesand act like particles (energy is given off in packets, called photons) perhaps matter, which is composed of particles can act like waves. This became known as the Wave-Particle Duality, which led to Quantummechanics and the discussion that the electron, which is a particle, can move like a wave. mparticle = h /  v (v is velocity) h = 6.626 x 10-34 Js = wavelength in m m = mass in kg v = velocity in m/s particle = h / m v

30. An electron has mass, so it is matter. A particle can only go through one hole, a wave through both holes. An electron does go through both, and makes an interference pattern. Thus, it behaves like a wave. Electrons exhibit wave like properties – they can pass through each other! Phenomenon of electron interference In fact in 1927, a beam of electrons was able to be diffracted thus suggesting that like light, electrons travel in waves. ONLY wavesCAN BE DIFFRACTED. (This experimental evidence helped prove de Broglie’s ideas.) NOTE: Because de Broglie’s hypothesis is applicable to all matter, any object has the characteristics of waves, however the wavelength of an ordinary sized object, such as a golf ball, is so tiny, that it cannot be observed by the human eye.

32. Dual Nature of Light Waves can bend around small obstacles… …and fan out from pinholes. Particles effuse from pinholes Three ways to tell a wave from a particle… wave behavior particle behavior waves interfere particle collide waves diffract particles effuse waves are delocalized particles are localized

33. This quantum picture of the world is at odds with our common sense view of physical objects. We cannot uniquely define what is a particle and what is a wave !!

34. TRUE UNDERSTANDING OF NATURE REQUIRED THAT PHYSICAL OBJECTS, WHATEVER THEY ARE, ARE NEITHER EXCLUSIVELY PARTICLES OR WAVES No experiment can ever measure both aspects at the same time, so we never see a mixture of particle and wave. WHEN ONE OBSERVES A PHYSICAL PHENOMENON INVOLVING A PHYSICAL OBJECT, THE BEHAVIOUR YOU WILL OBSERVE – WHETHER PARTICLE LIKE OR WAVE LIKE – DEPENDS ON YOUR METHOD OF OBSERVATION. THE OBJECT IS DESCRIBED BY MATHEMATICAL FUNCT IONS WHICH ARE MEASURES OF PROBABILITY .

35. ALL PHYSICAL OBJECTS exhibit both PARTICLE AND WAVE LIKE PROPERTIES. THIS WAS THE STARTING POINT OF QUANTUM MECHANICS DEVELOPED INDEPENDENTLY BY ERWIN SCHRODINGER AND WERNER HEISENBERG.

36. Classical world is Deterministic: • Knowing the position and velocity of all objects at a particular time • Future can be predicted using known laws of force • and Newton's laws of motion. Quantum World is Probabilistic: • Impossible to know position and velocity with certainty at a given time. • Only probability of future state can be predicted using • known laws of force and equations of quantum mechanics. Tied together Observed Observer

37. BEFORE OBSERVATION IT IS IMPOSSIBLE TO SAY WHETHER AN OBJECT IS A WAVE OR A PARTICLE OR WHETHER IT EXISTS AT ALL !! QUANTUM MECHANICS IS A PROBABILISTIC THEORY OF NATURE

38. Heisenburg’s Uncertainty Principle In order to find the location or momentum (velocity) of the electron, the investigator must interact with the electron. Heisenberg’s uncertainty principle states you can never know both the location of an electron and its momentum (velocity). If you know the velocity, then you will not know the location; likewise, if you know the location, you cannot know the velocity. Scientists do not know the exact path that an electron will follow.

39. Heisenberg Uncertainty Principle • In order to observe an electron, one would need to hit it with photons having a very short wavelength. • Short wavelength photons would have a high frequency and a great deal of energy. • If one were to hit an electron, it would cause the motion and the speed of the electron to change. • Lower energy photons would have a smaller effect but would not give precise information.

40. The Quantum Mechanical Model • Charge Cloud Model • Erwin “Werner” Schrödinger • Austrian • Energy is quantized. It comes in chunks. • Schrödinger derived an equation that described the energy and position of the electrons in an atom.

41. Modern View • The atom is mostly empty space. • Electrons do not follow circular paths. • Energy levels are 3-dimensional. • Model is based on the probability of finding an electron a certain distance from the nucleus • Two regions • Nucleus- protons and neutrons. • Electron cloud- region where you might find an electron.

42. So, unlike the Bohr theory of the atom, the modern quantum theory of the atom does not show the electrons following circular orbits, but shows the regions in which there is a high probability of finding an electron. These regions are called orbitals (90% probability). This new theory of wave mechanics, or quantum mechanics, was credited to Erwin (Werner) Schrödinger. In your junior year in college, in physical chemistry you will spend 15 weeks studying the mathematics behind Schrödinger’s equation. (In fact, he was given the 1932 Nobel Prize in Physics for it.) These equations are used to determine the probability of finding a particle at a particular time and a particular place; hence, the locationof the electron. Schrödinger’s work shows how the probability of finding the electron varies within the atom. Electron cannot destructively interfere with itself

43. QUANTIZED WAVELENGTHS Standing Wave Fundamental mode Second Harmonic or First Overtone 200 150 100 50 0 - 50 -100 -150 -200 200 150 100 50 0 - 50 -100 -150 -200 200 150 100 50 0 - 50 -100 -150 -200 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200

44. Electrons as Waves QUANTIZED WAVELENGTHS n = 5 n = 4 n = 6 Forbidden n = 3.3

45. Schrodinger’s Cat

46. A compilation of individual electrons • The visual concept of the atom now appeared as an electron "cloud" which surrounds a nucleus. • The cloud consists of a probability distribution map • Determines the most probable location of an electron. • For example, if one could take a snap-shot of the location of the electron at different times and then superimpose all of the shots into one photo, then it might look something like the view at the top.

47. Scientists are able to plot the changing probability as points as a three-dimensional representation. You will find that regions with high probability have a dense set of points, while areas of low probability have points that are more spread out. These plots look like diffuse clouds. Thus leading to the present day name of the model of the atom, Charge-cloud. Solving various wave equations led us to the location and motion of the electron inside the atom. A set of four(4) quantum numbers describe the probability(orbitals) of finding the electron at a certain spot in the atom. Using these four quantum numbers, we are able to describe the energy level, sublevel, orbital, etc. of each electron.

48. Orbital Quantum Mechanics • Orbital (“electron cloud”) • Region in space where there is 90% probability of finding an electron 90% probability of finding the electron Electron Probability vs. Distance 40 30 20 Electron Probability (%) 10 0 0 50 100 150 200 250 Distance from the Nucleus (pm)

49. Shapes of s, p, and d-Orbitals s orbital p orbitals d orbitals

50. Atomic Orbitals