An Introduction to Quantum Mechanics - Particle Properties of Waves - Presentation

1. Modern Physics
Dr.N.Meenakshisundaram M.Sc., NET, Ph.D. (IITM)
Assistant Professor of Physics
Vivekananda College
Madurai - 625234

2. The Birth of Quantum Mechanics
Wave – Particle Duality

3. Particle Properties of Waves
● Introduction
● Photoelectric Effect
● Compton Effect

4. Established Theories in Physics
Analytical Mechanics
Thermodynamics
Maxwellian Electrodynamics
Till the Nineteenth Century

5. Let us examine the following
Our understanding of the physical world is that it is
made up of two basic distinct entities.
Waves:
Like sound waves, ripples on the surface of water,
electromagnetic waves.
Material objects:
Like a particle, a ball, a car, the planets.

6. Are they very different ?
Material Objects
• Can be located at a definite position at a
given time.
• Can be at rest or moving or accelerating
under an external force.
• When they collide, they either scatter or
shatter. They definitely cannot pass through
each other.

7. It would seem so.
Waves
• They are spread out in space and time.
• They are defined by their velocity, wavelength,
frequency or amplitude.
• They can pass through one another. In the process
the waves are either enhanced or reduced.

8. The Birth of Quantum Mechanics
• At the turn of the last century, there were several
experimental observations which could not be
explained by the established laws of classical
physics and called for a radically different way of
thinking
• This led to the development of Quantum
Mechanics which is today regarded as the
fundamental theory of Nature.

9. Some key events/observations that led to
the development of Quantum Mechanics…
• Black body radiation spectrum (Planck, 1901)
• Photoelectric effect (Einstein, 1905)
• Model of the atom (Rutherford, 1911)
• Quantum Theory of Spectra (Bohr,1913)

10. Some key events/observations that led to the
development of Quantum Mechanics…
• Scattering of photons off electrons (Compton, 1922)
• Exclusion Principle (Pauli, 1922)
• Matter Waves (de Broglie 1925)
• Experimental test of matter waves (Davisson and
Germer, 1927)

11. Einstein
Planck Rutherford
Bohr Compton

12. Pauli
de Broglie
Davisson and Germer

13. The Nature of Light…
• The birth of quantum mechanics is intimately
linked with the theories and discoveries relating to
the nature of light
• Is the nature of light that of a wave or a particle?

14. The Story of Light…
• Corpuscular theory (Newton)
• Wave nature (Huygens)
• Double-slit interference experiment (Young)

15. The Story of Light (contd.)….
• Light is an electromagnetic wave (Maxwell)
• Photoelectric effect – existence of light quanta –
photons (Einstein)
• Photons have momentum (Compton)…..

16. Newton Huygens Youn
g
Maxwell Einstein Compton

17. Light has a Dual nature
• Wave (electromagnetic) - Interference
- Diffraction
• Particle (photons) - Photoelectric effect
- Compton effect
“Wave - Particle Duality for light”

18. Wave
Our traditional understanding of a wave….
“de-localized” – spread out in space and time

19. Particle
Our traditional understanding of a particle…
“Localized” - definite position, momentum
and confined in space

20. The connecting link – Planck’s
constant
Dual Nature
Radiation -
Matter -

21. What about Matter?
If light, which was traditionally understood as a
wave also turns out to have a particle nature,
might matter, which is traditionally understood as
particles, also have a wave nature?
Yes!

22. Particle Properties of Waves

23. Photoelectric Effect
“The energies of electron liberated by
light depend on the frequency of the light”
During his experiments on electromagnetic waves, Hertz noticed that
sparks occurred more readily in the air gap of his transmitter when
ultraviolet light was directed at one of the metal balls . He did not
follow up this observation, but others did. They discovered that the
cause was electrons emitted when the frequency of the light was
sufficiently high. This phenomenon is known as the photoelectric
effect and the emitted electrons are called photoelectrons.

24. Experimental Observation of
Photoelectric Effect
1. An evacuated tube contains two electrodes connected to a
source of variable voltage, with the metal plate whose
surface is irradiated as the anode.
2. Some of the photoelectrons that emerge from this surface
have enough energy to reach the cathode despite its
negative polarity, and they constitute the measured current

25. 3.The slower photoelectrons are repelled before they get to
the cathode.
4.When the voltage is increased to a certain value V0, of the
order of several volts, no more photoelectrons arrive, as
indicated by the current dropping to zero. This extinction
voltage corresponds to the maximum photoelectron kinetic
energy.
5. Light waves carry energy, and some of the energy
absorbed by the metal may somehow concentrate on
individual electrons and reappear as their kinetic energy.

26. Quantum Theory of Light
In 1905 Einstein realized that the photoelectric
effect could be understood if the energy in light is not
spread out over wave fronts but is concentrated in
small packets, or photons.
Each photon of light of frequency  has the energy
h, the same as Planck’s quantum energy.

27. Work Function
There must be a minimum energy Ф for an electron to
escape from a particular metal surface or else electrons
would pour out all the time. This energy is called the Work
Function of the metal, and is related by the formula .
The greater the work function of a metal, the more energy is
needed for an electron to leave its surface, and the higher the
critical frequency for photoelectric emission to occur.

28. Photoelectric Effect - Equation
where h is the photon energy, KEmax is the
maximum photoelectron energy (which is
proportional to the stopping potential), and  is
the minimum energy needed for an electron to
leave the metal.
KEmax =h(υ– υ0)

29. Compton Effect
In this observation

30. X-ray Photon strikes an Electron

32. We know that

35. What about Matter?
If light, which was traditionally understood as a
wave also turns out to have a particle nature,
might matter, which is traditionally understood as
particles, also have a wave nature?
Yes!

36. Dr. Quantum - Double Slit Experiment -Animation
https://youtu.be/Q1YqgPAtzho
Text book Reference
Concepts of Modern Physics - Arthur Beiser,
Sixth Edition 2004, Tata McGraw-Hill Publishing
Company Limited, New Delhi
Chapter 2 : 2.3 & 2.7
Acknowledgement
References collected from Google Search!!