 I, Dr. Mrs. Preeti Sunil Joshi, Assistant Professor from Department of Humanities and Sciences, Balchan Institute of Technology, Solapur. Welcome you in the session of Physics, which is related with Introduction to Quantum Mechanics. Learning outcomes of this session are, by the end, students will be acquaint with the developments in classical and quantum mechanics, will identify wave particle behaviour of matter, students will be able to understand de Broglie hypothesis and learn different properties of matter waves. The contents include introduction, wave particle duality, de Broglie hypothesis and properties of matter waves. The aim of physics is to understand the natural phenomena around us. 19th century witnessed a rapid growth in physics. Newtonian mechanics was nearly perfected and Maxwell synthesized the field of electricity and magnetism into a single theory which permitted inclusion of optics into the framework of electromagnetic phenomena. Towards the end of 19th century, it was generally believed that all that to be discovered in nature was discovered and all the laws of nature were formulated. The Newtonian mechanics, Maxwell's electromagnetic theory and thermodynamics came to be known as classical mechanics. At about turn of 20th century, a number of fundamental discoveries were reported which could not be explained within the framework of the above classical theories of physics. The inadequacy of classical theories was noticed first when they were applied to explain the blackbody radiation that is emitted by a body hotter than its surroundings. To explain blackbody radiation, Max Planck put forward a revolutionary hypothesis that the molecules in a source emit energy not continuously but in small discrete packets which are called as CONTA. This was a radical departure from the classical theory and contrary to day to day experience. After that, Einstein made use of Planck's hypothesis that a quantum of radiation carries an energy h nu and successfully explained the photoelectric effect. Other experimental results also showed that classical concepts were entirely inadequate and one has to invoke the quantum concept to explain the behavior of atoms and subatomic particles. A new body of ideas based on Planck's work was developed and a new theory came to be known as quantum physics. So the objects or matter can either be particles or they can be waves. And so scientists have found that there is this duality. Waves act like waves and waves act like particles. So before we talk about we should identify what a particle is and what a wave is. They are both ways that we can transfer energy from one point to another. So that is a particle when energy transfer takes place from one point to another and in case of wave we can see that the wave continues to move back and forth. This is transferring energy through the medium and in this video we are going to talk about how particles have wave properties. But it will show you what is going on in the world of very small the world of quantum mechanics. So well we live in the world of classical mechanics, we live in a world where everything travels much less than the speed of light and the things are much larger than the size of an atom. But when things really get fast we have to adjust and use relativistic mechanics. And as things get really really very small we have to use quantum mechanics. So quantum physics explain the behavior of matter and radiation at the microscopic level and quantum mechanics is the study of mechanical systems whose dimensions are close to the atomic scale. The interactions between atoms are governed by quantum mechanics and so an understanding of quantum mechanics is must for understanding the science. Quantum mechanics does not explain how a quantum particle behaves. Students, now please pause the video and answer these multiple choice questions. Check for the correct answers. So we have seen that Einstein had shown that photons are not only waves but they are particles using the photoelectric effect and he even calculated the energy of photon. While De Broglie proposed that the matter is made up of waves and gave the formula where wavelength of matter is equal to Planck's constant divided by momentum. So if mass is large the wavelength is small and as mass gets smaller you end up getting is matter acting like a wave. So we know that the matter is both a particle and a wave. It has just like light, this wave particle duality. If we are dealing with matter as particle we call that classical mechanics or classical physics and if we are dealing with a wave then it is quantum mechanics. But how do we know just like light which kind of model should we use? It all comes down to scale. If we are dealing with the microscopic so this is everything that is even microscopic then it is going to be classical mechanics. But when we have to move down to the level of nanoscopic really small particles then we deal with matter as a wave. And then De Broglie wavelength tells us you know how much wavelength effect we are going to have. In 1924 Louis De Broglie extended the wave particle dualism of light to the material particles. He reasoned out that nature exhibits a great amount of symmetry. Therefore if a light wave can act as a wave sometimes and as a particle at other times then particles such as electrons also act as waves at times. This is known as De Broglie hypothesis. According to De Broglie hypothesis any moving particle is associated with a wave. The waves associated with particles are known as De Broglie waves or Miter waves. The wavelength lambda of matter waves associated with a particle moving with velocity v is inversely proportional to the magnitude of the momentum of the particle. Thus lambda is equal to H upon Mv. As photon travels with velocity c its momentum is given by p is equal to e upon c therefore p is equal to Hv upon c therefore momentum is equal to H upon lambda. Thus the wavelength and momentum p of a photon are related to each other through an expression lambda is equal to H upon p. By this equation number 3 De Broglie proposed that the relation between the momentum and the wavelength of a photon is universal one and it must be applied to photons and material particles as well. Though the quantities nu and lambda are pure properties and the quantities e and p are particle properties they are related to each other. By the equation number 4 which shows that wave and particle nature of a photon are interrelated to each other. Now let us consider a moving particle having mass m velocity v and momentum p then equation 5 that is p is equal to m into v and it must be associated with a wave of wavelength equation number 6 that is lambda is equal to H upon p. The waves associated with moving particles are called matter waves or De Broglie waves. The relation equation 7 that is lambda is equal to H upon Mv is called as De Broglie equation and the wavelength lambda is called as De Broglie wavelength. So the conclusions can be made from the equation lambda is equal to H upon Mv as when the velocity of the particle is 0 lambda is equal to infinity which means that matter waves are detectable only for moving particles. Wave behavior of micro particles will be significant whereas waves associated with the macro bodies can never be detected because lighter the particle smaller is mass and hence longer is the wavelength of matter waves that is associated with it. The smaller the velocity of the micro particle the longer is the wavelength of the matter waves associated with it. Now let us see De Broglie wavelength associated with an accelerated charged particle. If a charged particle such as electron is accelerated by a potential difference v then its kinetic energy is given by e into v which is equal to half Mv square therefore v is equal to root 2 e v by M then the electron wavelength is given by after simplification lambda is equal to H upon root 2 em into v. Now consider if a particle has kinetic energy Ke then kinetic energy is equal to half Mv square is equal to M square v square upon 2 into M so p square upon 2 M hence lambda is equal to H upon root 2 M multiplied by kinetic energy. If particles are in thermal equilibrium at temperature T then their kinetic energy is given by 3 by 2 kT therefore lambda is equal to H upon root 2 M kinetic energy so the wavelength is equal to H upon root 3 M into k into T. So the properties of matter waves can be matter waves are produced by the motion of the particles and are independent of the charge therefore they are neither electromagnetic nor acoustic waves but they are a new kind of waves. The smaller the velocity of the particle the longer is the wavelength of matter waves that is associated with it. They can travel through vacuum and they do not require any material medium for their propagation. The velocity of matter waves depends on the velocity of the material particle and is not a constant quantity. The lighter the particle the longer is the wavelength of the matter waves associated with it. The velocity of matter waves is greater than the velocity of light. And lastly the exhibit diffraction phenomena as any other waves. Students, now please pause the video and solve the numerical, please check for the correct answer. Thank you.