Lecture 15

1. Quantum Theory of Light. Matter Waves. Photoelectric effect Photons De Broglie Waves Uncertainty Principle Lecture 15

2. Modern and Classical Physics Classical physics treats particles and waves as different aspects of the reality. However, the physical reality arises from small-scale world of atoms and molecules, electrons and nuclei. Electrons behave as particles because they have charge and mass, but moving electrons also show evidence of behaving as waves (diffraction, interference). The wave-particle duality is central to an understanding of modern physics.

3. Experiments showed that light directed onto a metal surface causes the surface to emit electrons. This phenomenon is called photoelectric effect. Photoelectric Effect • 3 features of photoelectric effect: • The electron is always emitted at once even under a faint light. • A bright light causes more electrons to be emitted than the faint light, but the average kinetic energy of the electrons is the same. • The higher the light frequency, the more kinetic energy the electrons have.

4. Photons The electromagnetic theory of light could not explain the experimental results concerning photoelectric effect. In 1905 Albert Einstein created the quantum theory of light. Einstein proposed that light consists of small separate bursts of energy called photons. In 1900 Max Planck proposed that hot objects contribute energy in separate units, called quanta, to the light they produce.

5. Photons E = hf E = quantum energy, f = frequency, h= Planck’s constant h = 6.63 1034 Joule second (J s) Einstein suggested that some minimum energy (w) is needed to pull an electron away from a metal. If the quantum energy E < w, no electron comes out. hf = KE + w Photons have properties of particles: localized in a small region of space, have energy and momentum, and interact with other particles (like billiard balls).

6. X-rays The wave theory of light and the quantum theory of light complement each other. In 1895 Wilhelm Roentgen discovered inverse photoelectric effect. He observed glowing of a fluorescent screen under a bombardment by electrons. The discovered radiation was very penetrating and was called X-rays. X-rays are produced whenever fast electrons are suddenly stopped. They turned out to be electromagnetic waves of extremely high frequency.

7. Matter Waves In 1924 Louis de Broglie suggested that moving objects in some respects act like waves. A particle of mass m and speed v behaves like a wave with wavelength , so that h Plank’s constant  = ------  de Broglie wavelength = -------------------------- mv momentum Later it was shown that electrons exhibit both diffraction and interference, and their wavelengths are in agreement with the de Broglie wavelength.

8. Wave Function In water waves, the height of the water surface varies. In sound waves, it is the air pressure. In electromagnetic waves, it is electric and magnetic fields. In matter waves, the wave function  (psi) varies.  2 at a given place and time for a given particle determinesthe probability of finding the particle there at that time.  2 is called the probability density of the particle.

9. Uncertainty Principle If a moving particle is a wave, then there are limits on the accuracy of the measurements of its position and speed. The particle may be located anywhere within the wave packet at a given time. The maximum of  2 is in the middle of the packet. However, the particle can be found anywhere that  2  0. The uncertainty principle: It is impossible to know both the exact position and the exact momentum of a particle at the same time.

10. Summary The discovery of the photoelectric effect gave rise to the quantum theory of light. Matter can also behave as a wave, like electromagnetic waves can behave as particles. The uncertainty principle is one of the most significant physical laws. It implies that we cannot now future for sure because we cannot know the present for sure. Importance of the subject