Part 2: Quantum* Mechanics

Transcription

1 Part 2: Quantum* Mechanics Courtesy of IBM *We say something is quantized if it can occur only in certain discrete amounts.

2 Quantum Mechanics is the greatest intellectual accomplishment of human race. - Carl Wieman, Nobel Laureate in Physics 2001 To understand something means to derive it from quantum mechanics, which nobody understands unknown origin

3 Part 2 of this course: 1. Basic properties of light (electromagnetic waves). 2. Photoelectric effect and how it shows light comes in quantized units of energy. When is a wave not a wave? (When it is a particle!) 3. Atomic spectra- quantized energy of electrons in atoms. 4. Bohr model of the atom. Where it works. Why it is wrong. 5. de Broglie idea- wave-particle duality of electrons etc. When is a particle not a particle? (When it s a wave). 6. Schrodinger Equation and quantum waves. 7. What they are, how to use. 8. Applications: chemistry, electronics, lasers, MRI,

4 Today (and next class): Basic properties of light ( electromagnetic waves ): How to generate light Wave-like properties of light Next class: Particle-like properties of light Disclaimer: A very exciting part of this course is the particle-wave duality (of light and matter)! It might seem confusing when to use the wave or the particle representation of the very same physical entity. But in the end it simply depends on the experiment ( question or measurement )! We will see several experiments that will help you understand this exciting concept. Strap in and enjoy the ride!

5 Properties of light à Interaction with matter When does an electric field exert a force on a charge? a) Always b) Sometimes (only static electric fields) c) Sometimes (only alternating fields) d) Sometimes (depends on the sign of the charge) e) Never or only rarely

6 Properties of light à Interaction with matter Electric fields exert forces on charges E F=qE + _ E F=qE (e s and p s in atoms) Force = charge electric field F= qe Light is an oscillating E(and B)-field. It interacts with matter by exerting forces on the charges (electrons and protons in atoms).

7 How do you generate light (electromagnetic radiation)? a. Stationary charges b. Charges moving at a constant velocity c. Accelerating charges d. b and c e. a, b, and c Stationary charges à constant E-field, no magnetic (B)-field E + Charges moving at a constant velocity à Constant current through wire creates a B-field But B-field is constant I B Accelerating charges à changing E-field and changing B-field (EM radiation à both E and B are oscillating) B E

8 Electrostatic fields Charges-and-fields.jar

9 Electromagnetic waves Radio Waves.jar

10 The sun produces lots of light Why? How? Surface of sun- very hot! Whole bunch of free electrons whizzing around like crazy. Equal number of protons, but heavier so moving slower, less EM waves generated by protons.

11 Remember this one? Light source E E E-field (for a single color): E(x,t) = E 0 sin(kx ωt + φ) λ = 2πc/ω, φ λ ω = 2πf = 2π/T k = 2π / λ E 0 Wavelength λ of visible light is: λ ~ 350 nm 750 nm. x B x

12 Making sense of the Sine Wave CQ: What does the curve tell you? -For Water Waves? -For Sound Wave? -For E/M Waves?

13 Snapshot of radio wave in air. Length of vector represents strength of E-field Orientation represents direction of E-field What stuff is moving up and down in space as radio wave passes? a. protons b. electrons c. air molecules d. light ray e. nothing E. answer is nothing! Electric field strength increases and decreases E-field does not move up and down.

14 Electromagnetic Spectrum Spectrum: All EM waves. Complete range of wavelengths. Cosmic rays SHORT LONG

15 EM radiation often represented by a sinusoidal curve. OR CQ: What does that sinusoidal curve tell you? a.the motion of electrons in the atmosphere when the EM wave passes. b.the motion of air molecules when the EM wave passes. c. The actual path the light travels through space. d.the E-field s direction and strength along the center line of the curve. e.none of the above.

16 EM radiation often represented by a sinusoidal curve. CQ: What does the curve tell you? Correct answer is d: The E-field s direction and strength along the center line of the curve At this time, E-field at point X is strong and it points upward. Only know E-field, along this line. X Path of EM Radiation is a straight line.

17 Today (and next class): Light is a wave! Oh no, it s a particle! Or is it?

18 Maxwell s Equations: Describes EM radiation E d A = Q in ε 0 E d s = d Φm dt B d A = 0 B d s = µ I + ε µ 0 through 0 0 dφ dt e B E

19 Maxwell s Equations: Describes EM radiation E d A = Q in ε 0 E d s = d Φm dt B d A = 0 B d s = µ I + ε µ 0 through 0 0 dφ dt e In 3-D: 2 1 E = c 2 2 t E 2 In 1-D: 2 x E 2 = 1 c 2 2 t E 2 Show that E(x,t) = E max cos(ax+bt) (in 1-D) with b/a=c. (Homework) is a solution

20 Electromagnetic waves carry energy E max =peak amplitude c E max E(x,t) = E max sin(ax-bt) X Light shines on black tank full of water. How much energy absorbed? Intensity = Power = energy/time α (E max ) 2 α (amplitude of wave) 2 area area Intensity only depends on the E-field amplitude but not on the color (or frequency) of the light!

21 How can we see that light really is a wave? During s: lot s of debate about what light really is. After ~1876 (Maxwell): Light = EM radiation viewed as a wave. But how can it be tested? What is most definitive observation we can make that tells us something is a wave? Observe interference!! (Remember the Michelson interferometer?)

22 Interference of EM waves Constructive interference: Peaks and valleys are lined up c Fields add up!

23 Interference of EM waves Destructive interference: Peaks and valleys cancel each other c Fields cancel!

24 Two slit interference

25 Two slit interference wave interfarence online wave-interference_en

26 Light is a wave à interference! The definite check that light IS a wave Observe interference! wave-interference_en.jar

27 That's all about EM waves (for now) Questions?

28 So we found: light is a wave! and things start to make a lot of sense: EM waves can are described by Maxwell's theory Double slit experiment and other diffraction phenomena can be explained. Explains grating spectrometers etc. But then there was this one, little experiment from Mr. Hertz (~1887) that just couldn t be explained with EM waves!... Actually, some other problems started to surface, such the lack of an accurate model for the black body radiation

29 The photoelectric effect (~1900) The photoelectric effect is a phenomenon in which electrons are emitted from matter as a consequence of absorbing energy from light. The effect was only observed with UV light, but not so with red or IR light. à Effect is frequency dependent!? But Mr. Maxwell told us that the light intensity doesn t depend on frequency! (Intensity only depends on E 2 ) Is Mr. Maxwell wrong this time?? He was right last time

30 Electromagnetic waves carry energy E max X #1 X #2 E 1max =E 2max >E 3max f 1 = f 3 < f 2 X #3 Which barrel will heat up the fastest? a. 2>1>3 b. 1>2>3 c. 1=2>3 d. 1=3>2 e. 2>1=3 Intensity = power/area α E 2 max Does not depend on frequency/color!

31 Electromagnetic waves carry energy E max =peak amplitude c E max E(x,t) = E max sin(ax-bt) X Light shines on black tank full of water. How much energy absorbed? Intensity = Power = energy/time α (E max ) 2 α (amplitude of wave) 2 area area Intensity only depends on the E-field amplitude but not on the color (or frequency) of the light!

32 Today: The Photo Electric Effect

33 The photoelectric effect (~1900) The photoelectric effect is a phenomenon in which electrons are emitted from matter as a consequence of absorbing energy from light. The effect was only observed with UV light, but not so with red or IR light. à Effect is frequency dependent! But Maxwell told us that the light intensity doesn t depend on frequency! (Intensity only depends on E 2 )

34 Experimental apparatus: PE effect Metal surface Glass cylinder Vacuum

35 Experimental apparatus: PE effect Metal surface Glass cylinder Vacuum Adjustable voltage Current meter

36 What happens? A B - 10 V + 2 ohms Two metal plates in vacuum with a voltage between them. How much current is flowing through the resistor? A) 0 A B) 0.2 A C) 5 A D) 10 A E) infinite current

37 What happens? A B - 10 V + 2 ohms Two metal plates in vacuum with a voltage between them. The potential difference between A and B is: A) 0 V B) 5 V C) 10 V D) infinite volts