Quantum Mechanical Model of the Atom PDF 2025

QUANTUM MECHANICAL MODEL OF THE ATOM  Introduction The simple Bohr model was unable to explain properties of multi electrons atoms Only worked for hydrogen A new model was needed…  By the 1920’s, scientists were convinced that Bohr’s model was fundament...

QUANTUM MECHANICAL MODEL OF THE ATOM  Introduction The simple Bohr model was unable to explain properties of multi electrons atoms Only worked for hydrogen A new model was needed…  By the 1920’s, scientists were convinced that Bohr’s model was fundamentally incorrect. New explanations of how electrons were arranged in atoms were needed.  Quantum Mechanics the application of quantum theory to explain the properties of matter, particularly electrons in atoms  Learning goals Describe the contributions of De Broglie, Schrodinger and Heisenberg to the development of the Quantum mechanical model of the atom What was known at that time? Light has a dual nature – it can behave as a wave and as a particle Dual nature of matter De Broglie knew that when light traveled through space, it behaved like a wave. He also knew that when light interacted with matter, its behavior was like that of a stream of particles. He thought that if energy had a dual nature then maybe matter did too…  De Broglie contribution Louis de Broglie, a French physicist, originated the idea that the electron, previously considered just a particle, has wave properties.  Wave nature of matter De Broglie believed that all moving particles of matter, like electrons, had wave characteristics. He referred to the wavelike behavior of particles as matter waves.  Not all objects show wave properties Only very light objects show wave properties Life-sized objects do not show any wave behaviour Why? Broglie found that the wavelength is inversely proportional to the mass  Heavy objects produce very small, negligible wavelengths – cannot be detected not detected Very light objects produce large wavelengths – can be detected Wave-like properties are more significant for objects of very low mass such as electrons RECAP All matter has both wave and particle properties Wave-like properties are more significant for objects of very low mass such as electrons Quantum Mechanical Model In 1926, Erwin Schrodinger furthered the wave-particle theory of de Broglie. He derived a mathematical equation that described hydrogen atom’s electron as a This equation is called the Schrodinger’s wave equation and is used to calculate electron energy levels  Quantum Mechanical Model The atomic model in which the electron is treated as a wave is called the quantum mechanical model of the atom.  The electron bound to a nucleus resembles a circular standing wave This circular standing wave consists of wavelengths that are multiples of whole numbers Since the wavelength of an electron must be a whole number, only certain electron energies are allowed(quantized). Electrons can only have certain wavelengths Only certain circular orbits have a  The circumference of a particular orbit corresponds to a whole number of wavelengths. Any other orbits of the standing electron wave are not allowed because they would cause the standing wave to cancel out or collapse, that is, undergo destructive interference This model explains the observed quantization of the hydrogen atom- meaning only certain electron energies are allowed the whole-number multiples of wavelengths correspond to multiples of fixed quanta of energy that the electron can have in the Louis de Broglie's explanation of Bohr's atomic model video https://www.youtube.com/watch?v=o Ld-6UytkIU However, the new question that this model raised was this: where is the electron located in the hydrogen atom? Heisenberg’s Uncertainty Principle In 1927, Werner Heisenberg proposed his uncertainty principle: it is impossible to know both the exact position a speed of an electron at a give time. He believed any attempt to determine an electron’s positio would change its speed and vice versa. Heisenberg’s uncertainty principle Life-sized objects are easy to locate because you can see them You can determine both speed and location of a moving car using a radar gun and a GPS unit The energy from the radar waves will not affect its path because it is massive Slo w Fast Heisenberg’s Uncertainty Principle For atomic-sized particles any attempt to probe them changes their position, direction of travel or both The best we can do is to describe the probability of finding an electron in a specified location Effect of Heisenberg Uncertainty Principle The effect of the Heisenberg uncertainty principle is significant only for motion of subatomic particles like ___electrons_________ and for life-sized objects like __cars_____ , it is _____negligible__________ Analogy-Heisenberg’s Uncertainty Principle Suppose you had to locate a helium-filled balloon in a dark room. To locate it, you would touch it with your hand. Such an act would cause a change in the speed of the balloon. Hence, you cannot know the position and speed at the same Heisenberg’s Uncertainty Principle But what if you used a flashlight? You would locate the balloon when the light bounced off it and hit your eyes. The balloon is so much more massive than the photons that they will have “no Heisenberg’s Uncertainty Principle What about locating electrons? Could they be hit with a photon (which would then bounce back to some detection device)? No - Heisenberg’s Uncertainty Principle applies. Because the electron has such a small mass, its collision with a photon would change its position and speed. Heisenberg Principle video https://www.britannica.com/video/1 86244/video-overview-uncertainty- principle-Heisenberg  Recap What we know so far The energy of electrons is quantized. (Electrons can only have certain amounts of energy.) Electrons exhibit wavelike characteristics and behavior. We cannot experiment with electrons to determine their nature - position and speed of an electron are impossible to know at the same time. The best we can do is to describe the probability of finding an electron in a specific location Quantum Mechanics of the Electron https://www.youtube.com/watch?v =t8mMN2X5_Vw  Solutions to Schrodinger’s wave equation Schrodinger’s equation can be solved to obtain wave functions which describe the location in space (x, y, z) where an electron is likely to be found. These regions are known as orbitals.  Wave Function A mathematical probability of finding an electron in a certain region of space we cannot predict the electron’s location. Quantum mechanics does not describe how an electron moves or even if it moves It only tells us the statistical probssbility of finding the electron in a given location in an atom Wave function A mathematical probability of finding an Electron in a certain region of space  Electron An orbital is a 3d region around the nucleus Orbital where there is a high probability of finding an electron. Because electrons have different energies, they are found in different probable locations around the nucleus Orbitals have different shapes, sizes and energies.  Analogy for an orbital An electron orbital is analogous to students at school moving from classroom to classroom during a scheduled break. The students are like electrons, the school is like the atom, and the classrooms are like orbitals. Someone who does not know a student’s exact schedule may be able to determine the probability of that student  Another analogy with more appropriate relative sizes is a bee in a closed stadium. You know that the bee is inside the stadium, and you can reason that it will most likely be near its nest. However, you cannot pinpoint its exact location.  Electron Probabilty density Using wave functions, physicists have created a three-dimensional electron probability density, which is a plot that indicates regions around the nucleus with the greatest probability of finding an electron  ELECTRON PROBABILITY DENSITY The probability of finding an electron at a given location derived from wave equations used to determine the shapes of the orbitals also called electron probability distribution  The electron probability density plot for a hydrogen electron in the ground state (lowest energy state) is spherical and is called the 1s orbital Probability distribution of for the 1s orbital Electron probability density of various orbitals  Electron clouds Although we cannot know how the electron travels around the nucleus we can know where it spends the majority of its time (thus, we can know position but not trajectory). The “probability” of finding an electron around a nucleus can be calculated. Relative probability is indicated by a series of dots, pictured as a “electron cloud”. Quantum Mechanical Model An electron’s energy is limited to certain values. An electron’s path around the nucleus is not circular but is described in terms of probability. The probability of finding an electron in various locations around the nucleus can be pictured Quantum Mechanical Model The cloud is most dense where the probability of finding the electron is highest. The boundary of the “electron cloud” encloses the area that has a 90% probability of containing  An electron cloud represents the area around an atom's nucleus where electrons are most likely to be found.  Orbits Orbitals - 2n2 electrons - 2 electrons - circular or elliptical path - no set path - 2 dimensions - 3-dimensional space - Electron is a fixed - Electrons are a variable distance from nucleus distance from nucleus - 2n2 electrons - 2 electrons per orbital  Summary Louis de Broglie originated the idea that the electron has both particle and wave properties. The quantum (wave) mechanical model describes an electron as a standing wave. The electron can occupy a series of orbitals. Each orbital has a prescribed possible energy value and spatial distribution  The exact position of the electron and how it is moving can never both be known. This is consistent with Heisenberg’s uncertainty principle, which states that it is impossible to know both the position and the speed of a particle simultaneously  Orbitals are described as probability distributions and depicted as electron density plots. In the ground state, the single electron in a hydrogen atom resides in a low-energy orbital. The two main ideas of the quantum mechanical model of the atom are that electrons can move between orbitals by absorbing or emitting quanta of energy, and that the location of electrons is given by a probability distribution.  QUANTUM MECHANICAL MODEL The region around the nucleus where an electron has a high probability of being found is called an orbital. Electrons can move between orbitals by absorbing or emitting a quanta of energy The location of the electron is given by a probability distribution  Quantum Mechanics and the Schrödinger Equatio https://www.youtube.com/watch?v=O6g-7r Ugrdg&t=253s