Classical ConceptsEquations Newton’s Law Kinetic Energy Momentum Momentum and Energy Speed of light Velocity of a wave Angular Frequency Einstein’s Mass-Energy relation

Quantum (Modern) Physics Classical Mechanics Based on Newton’s laws Explains the large scale experiments (macroscopic scales) Fails to explain the different phenomena which takes at microscopic or atomic scales Quantum Mechanics Can explain the nature of light waves in terms of photons Phenomena like interference, diffraction, polarization are explained based on the wave nature of light Phenomena like photoelectric effect, Compton effect, Zeeman effect are explained based on the particle nature of light Wave-particle property of light radiation is known as the dual nature of light

There are always two contradictory theories about light Theory of Particles Theory of Wave Particle theory explain the fact that light travels in a straight line and reflects on the surface (cannot explain the refraction and diffraction of light) Nature of Light Wave character of light was clearly demonstrated in the reflection, refraction, and diffraction of light

Development of Quantum Theory Planck’s Theory In 1900, Max Planck showed that a successful theory of radiation was possible by making a assumption regarding the way in which radiation is emitted or absorbed Planck assumed that energy could only be emitted or absorbed as a radiation of frequency “ν” in integral multiples of “n” According to Planck’s theory, radiant energy is emitted or absorbed as quanta of light

Development of Quantum Theory Einstein and Bohr applied this concept to problems of photoelectric emission and structure of the atom Einstein interpreted the photoelectric equation by postulating that light always comes in the form of small packets of energy (quanta of light or photons) Bohr postulated that emission or absorption of energy corresponds an electron makes transition from one orbit to another by absorbing or emitting a photon of energy equal to the energy difference between the two states

Development of Quantum Theory Particle’s nature Planck’s theory of Black Einstein’s photoelectric effect Bohr’s line spectra Compton’s scattering These experiments showed the particle nature of radiations Wave Nature Electromagnetic radiations (visible, IR, UV, X-rays and gamma rays) were shown to have wave nature by interference and diffraction experiments

de Broglie Wave Radiation exhibits a dual wave-particle nature In 1924, Louis de Broglie proposed the idea of matter waves (de Broglie wave) (i)The universe is made up of radiation and matter (ii)Experimental results show that light has a dual nature

De Broglie’s hypothesis could be applied to all matters Interference and Diffraction are wave characteristics (light and X-ray) Electrons as Waves Young’s double-slit experiment with electrons showed interference effect for the electrons showing the wave nature Electrons also showed Interference and Diffraction Electron beam is diffracted by a thin polycrystalline gold film similar to X-ray diffraction predicted by Bragg’s law

de Broglie Wave According to de Broglie, light waves behave some times as particles and particles can have wavelike characteristic properties Particles like electrons, protons, neutrons, atoms or molecules will have associated waves with them called as matter waves A variable quantity known as wave function is used to characterize the de Broglie waves Wave function is denoted by the symbol Ψ (psi)

de Broglie Wavelength 1.de Broglie used famous Einstein’s mass-energy equation 2.Using Planck’s theory (Every quantum of a wave has a discrete amount of energy given by Planck’s equation) 3.Since de Broglie believed particles and wave have the same traits, he hypothesized that the two energies would be equal 4.Because real particles do not travel at the speed of light, de Broglie used the velocity as v instead of c

de Broglie Wavelength It is clear that the light photon with wavelength λ & momentum p = h / λ will have an associated wavelength λ and also a wavelike character In 1924, de Broglie suggested that the matter particles will have associated waves known as de Broglie waves or matter waves (de Broglie wavelength of the matter wave)

de Broglie Wavelength in terms of KE Consider a particle of mass m moving with a velocity v Kinetic Energy of the particle de Broglie wavelengthde Broglie wavelength in terms of KE

de Broglie Wavelength in terms of V Consider an electron of mass m and charge e, accelerated through a potential difference of V volts KE of the electrons is equal to the energy of the electron accelerated at a potential of V volts de Broglie wavelength of electron

Fifth International Congress of Physics in 1927 v v Einstein De Broglie Compton Bohr Heisenberg Schrodinger Bragg