09 Quantum Theory Grey

Corpuscular Theory of Light (1704)

Quanta: Particles, Waves, and Wave-Particles

● Isaac Newton proposed that light consists of a stream of small particles, because it z

travels in straight lines at great speeds

z

is reflected from mirrors in a predictable way

Newton observed that the reflection of light from a mirror resembles the rebound of a steel ball from a steel plate 2

Wave Theory of Light (1802)

Particles

● Young and Fresnel showed that light is a wave, because it

● Position x

z

undergoes diffraction and interference (Young’s double-slit experiment)

● Mass m ● Momentum p = mv

3

4

Waves

Waves versus Particles

● Wavelength λ

● A particle is localised in space, and has discrete physical properties such as mass ● A wave is inherently spread out over many wave-lengths in space, and could have amplitudes in a continuous range ● Waves superpose and pass through each other, while particles collide and bounce off each other.

● Amplitude A ● Frequency f z

number of cycles per second (Hertz) f=c/λ

5

6

1

Blackbody radiation depends on temperature

Blackbody Radiation ● A blackbody is an object which totally absorbs all radiation that falls on it ● Any hot body radiates light over the wide spectrum of frequencies. (examples: light bulbs, stars.) ● Blackbody radiation is the specific pattern emitted by a heated blackbody.

Plot of intensity of the blackbody radiation versus wavelength for various temperatures

Plot of intensity of the blackbody radiation versus frequency for various temperatures

7

Ultraviolet Catastrophe

8

Planck’s Quantum Postulate (1900) ● A blackbody can only emit radiation in discrete packets or quanta, i.e., in multiples of the minimum energy: E = hf, where h is a constant and f is the frequency of the radiation

Classical wave theory of light predicts a graph that deviates from experimental data, especially at short wavelengths – the ultraviolet catastrophe.

Max Planck (1858-1947) is generally regarded as the father of quantum theory 9

Planck’s Quantum Postulate (1900)

10

Planck’s Constant ● Experimentally determined to be h = 6.63 x 10-34 Joule sec (Joule = kg m2 / sec2) ● A new constant of nature, which turns out to be of fundamental importance in the new ‘quantum theory’

Result: A radiation law in extremely good agreement with experiment 11

12

2

Photoelectric effect: What is it?

Photoelectric effect experiment

Light falling on a metallic surface can eject electrons from the surface.

13

Photoelectric response to blue light

14

Photoelectric response to red light

When blue light is shone on the emitter plate, a current flows in the circuit

But for red light, no current flows in the circuit 15

16

Wave theory of light conflicts with detailed PE observations

Experimental Observations ● Only light with a frequency greater than a certain threshold will produce a current. ● Current begins almost instantaneously, even for light of very low intensity. ● Current is proportional to the intensity of the incident light.

17

● The energy of waves depends only on intensity and not frequency. Therefore, the color of light used should not affect the results of the photoelectric effect. ● This implies that a current should be produced when say, high-intensity red light is used – but experiments show it is not.

18

3

Einstein’s Explanation

Everyday Evidence for Photons

(1905)

● Light consists of particles, now known as photons. ● A photon hitting the emitter plate will eject an electron if it has enough energy ● Each photon has energy: E = hf

● Red light is used in photographic darkrooms because it is not energetic enough to break the halogen-silver bond in black and white films. ● Ultraviolet light causes sunburn but visible light does not because UV photons are more energetic. ● Our eyes detect color because photons of different energies trigger different chemical reactions in retina cells

Albert Einstein won a Nobel Prize for his work on the photoelectric effect and not his theory of relativity!

(same as Planck’s formula)

19

20

In summary...

Just a minute.

● Planck: Blackbody radiation demonstrates that matter emits light in discrete packets. ● Einstein: Photoelectric effect demonstrates that matter absorbs light in discrete packets. ● Light may propagate as a wave, but it behaves as a particle when it interacts with matter (absorption and emission).

● If a “light wave” can behave like a particle, can a particle of matter behave like a wave?

21

22

Double-Slit Experiment

Double-Slit Experiment

illustrates the wave nature of light

with a machine gun!

23

24

4

Double-Slit Experiment

Interference Pattern of Electrons

with electron gun

● Determines the probability of an electron arriving at acertain spot on the screen

?

● After many electrons, resembles the interference pattern of light

Electron interference pattern after (a) 8 electrons, (b) 270 electrons, (c) 2000 electrons, and (d) 6000 e

25

Double-Slit Experiment

26

Summary

with electron gun Electrons behave like waves!

● Waves and particles exhibit very different behaviour. ● Yet, light sometimes behaves like particles z

spectrum of blackbody radiation, photoelectric effect, other everyday examples

● And electrons sometimes behave like waves z de Broglie wavelength = h / mv 27

interference pattern of electrons

● In quantum theory, the distinction between waves and particles is blurred.

28

5