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 E n E n = 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

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

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

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

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

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 Li 2+

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