The Nature of Light

Is Light a Particle or a Wave?

2

The Particle Theory of Light Light is considered to be a stream of particles Isaac Newton was the chief architect of the particle

theory of light. Phenomena of light can be explained by the particle

theory Reflection, Refraction

Two phenomena of light can not be explained by the particle theory

Interference: The first demonstration by Thomas Young in 1801 Diffraction

3

The Wave Theory of Light In 1678, Dutch physicist, Christian Huygens,

showed a wave model of light that can explains also the reflection and refraction of light.

4

Diffraction

5

Interference: Young’s double-slit experiment

6

History of Wave Theory In 1801, Thomas Young provided the first clear

demonstration of the wave nature of light

In 1865, Maxwell asserted that light was a form of high-frequency electromagnetic wave and no medium is required for the propagation of light

In 1887, Hertz confirmed Maxwell’s predictions

During the 19-th century, other developments led to the general acceptance of the wave theory of light

7

New Phenomena support the Particle Theory of Light

Blackbody radiation

The photoelectric effect

The Compton scattering

Dual nature of light Now, we accept that light has a dual

nature.

In some cases, light behaves like a wave, and in others, light behaves like a particle.

8

9

Blackbody Radiation: Thermal radiation of a blackbody at T

10

Planck’s Theory of Blackbody Radiation

In 1900, Planck assumed the cavity radiation came from atomic oscillations in the cavity walls

Assumption (I): The energy of an oscillator can have only certain discrete values En

En = n h ƒ Assumption (II): The oscillators

emit or absorb energy only in discrete units

11

The photoelectric effect First discovered by Hertz The photoelectric effect occurs

when light incident on certain metallic surfaces causes electrons to be emitted from those surfaces

Einstein extended Planck’s concept of quantization to electromagnetic waves

All electromagnetic radiation can be considered a stream of quanta, now called photons

A photon of incident light gives all its energy hƒ to a single electron in the metal

12

The Compton Effect

The scattering of X-ray from free electron The results could be explained by treating

the photons as point-like particles having energy hƒ and momentum hƒ / c

13

Dual Nature of Light: Photons and Waves

Some experiments are best explained by the photon model

Some are best explained by the wave model The nature of light is not describable in terms

of any single classical model Light has a dual nature in that it exhibits both

wave and particle characteristics The particle model and the wave model of

light are complement each other

14

Wave Properties of Particles In 1923, de Broglie postulated that all matters

have both wave and particle properties The de Broglie wavelength of a particle is

The particles would also have a frequency

h h

p mv

ƒE

h

15

Davisson-Germer Experiment If particles have a wave nature,

they should exhibit diffraction effects

In 1927, Davission and Germer measured the wavelength of electrons by the diffraction of electrons from single crystals

This provided experimental confirmation of the matter waves proposed by de Broglie

16

Quantum Particle The quantum particle is a model for the dual nature

of light and of material particles In this model, entities have both particle and wave

characteristics We much choose one appropriate behavior in order to

understand a particular phenomenon

17

The Uncertainty Principle In classical mechanics, it is possible to

make measurements with arbitrarily small uncertainty

Quantum theory predicts that it is fundamentally impossible to make simultaneous measurements of a particle’s position and momentum with infinite accuracy

18

Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle states if a measurement of the position of a particle is made with uncertainty x and a simultaneous measurement of its x component of momentum is made with uncertainty p, the product of the two uncertainties can never be smaller than

2px x

19

Heisenberg Uncertainty Principle, Another Form

Another form of the Uncertainty Principle can be expressed in terms of energy and time

This suggests that energy conservation can appear to be violated by an amount E as long as it is only for a short time interval t

2tE

20

Wave Function – Probability Interpretation

The amplitude of the wave associated with the particle is called the probability amplitude or the wave function

The wave function is often complex-valued ||2 = is always real and positive

* is the complete conjugate of It is proportional to the probability per unit volume of

finding a particle at a given point at some instant The wave function contains within it all the

information that can be known about the particle

21

Schrödinger Equation for Wave function

Erwin Schrödinger proposed a wave equation that describes the manner in which the wave function changes in space and time

The Schrödinger equation for a particle of mass m confined in a potential energy function U(x) is

This is called the time-independent Schrödinger equation

2 2

22

h dU E

m dx

22

Quantum Tunneling Classically, the particle is

reflected by the barrier Regions II and III would be

forbidden According to quantum

mechanics, all regions are accessible to the particle

The probability of the particle being in a classically forbidden region is low, but not zero

Application: Scanning tunneling microscope

23

Early Models of the Atom – Newton’s Time

The atom was a tiny, hard indestructible sphere

It was a particle model that ignored any internal structure

The model was a good basis for the kinetic theory of gases

24

Early Models of the Atom – JJ Thomson

J. J. Thomson established the charge to mass ratio for electrons

His model of the atom A volume of positive

charge Electrons embedded

throughout the volume

25

Rutherford’s Thin Foil Experiment

In 1911, Rutherford performed an experiment to show that Tomson’s model was not correct

A beam of positively charged alpha particles hit and are scattered from a thin foil target

Large deflections could not be explained by Thomson’s model

26

Early Models of the Atom – Rutherford

Rutherford Planetary model Based on results of thin

foil experiments Positive charge is

concentrated in the center of the atom, called the nucleus

Electrons orbit the nucleus like planets orbit the sun

27

Difficulties with the Rutherford Model

Rutherford’s electrons are undergoing a centripetal acceleration

The electrons should radiate EM waves of the same frequency

The radius should steadily decrease as this radiation is given off

The electron should eventually spiral into the nucleus

Rutherford model is unable to explain certain discrete characteristic frequencies of EM radiation emitted by atoms

28

29.1 Importance of the Hydrogen Atom The hydrogen atom is the only atomic

system that can be solved exactly Much of what was learned about the

hydrogen atom, with its single electron, can be extended to such single-electron ions as He+ and Li2+

29

More Reasons the Hydrogen Atom is Important The hydrogen atom proved to be an ideal

system for performing precision tests of theory against experiment Also for improving our understanding of atomic

structure The quantum numbers that are used to

characterize the allowed states of hydrogen can also be used to investigate more complex atoms This allows us to understand the periodic table

30

Final Reason for the Importance of the Hydrogen Atom

The basic ideas about atomic structure must be well understood before we attempt to deal with the complexities of molecular structures and the electronic structure of solids