Introduction to Atomic Structure We are made of ATOMS ! Structure of the Atom Evolution of Atomic Theory First clear concept of Atom starts with the Jain School of Thought in th Century BC in India The Jains considered that matter is made of atoms or “paramanus” The Jain School also developed an elaborate set of theories on how atoms could combine, move, vibrate, etc In Western School, the concept of Atom starts in th Century BC through Ionian Philosopher Democritus The concept of atom was similar to Jain School in the sense that atoms were considered to be fundamental particles that can not be cut or broken into parts The word “atom” was coined by him from the Greek adjective “atomos” meaning uncuttable Atomistic philosophy in Islam was developed around 11 th century AD by Imam Ghazali synthesizing the Jain and Greek Schools of thoughts about Atom His atomic theory was more in tune with the Jain School rather than of the Greek School Towards late 18 th century scientific developments started renewed philosophical interest in composition of matter Dalton assimilated the experimental works of many scientists to propose his ultimate modern theory of matter known as Dalton’s Atomic Theory Dalton’s Atomic Theory Dalton’s Atomic Theory Elements are made of extremely small particles called atoms Atoms of a given element are identical in size, mass, and other properties; atoms of different elements differ in size, mass, and other properties Atoms cannot be subdivided, created, or destroyed Atoms of different elements combine in simple whole-number ratios to form chemical compounds In chemical reactions, atoms are combined, separated, or rearranged Dalton’s theory forms the foundation of Modern Theoretical Chemistry Thomson’s Plum Pudding Thomson’s Plum Pudding Model The model was proposed by Thomson in 1904 before the discovery of nucleus Electrons or “corpuscles” are floating in a soup of positive charge to balance the negative charges The positive charge was assumed to be like a “pudding”, and the negatively charged electrons as “plums” and hence the terminology Plum Pudding Model taken from a British dessert Rutherford-Geiger-Marsden gold foil experiment in 1909 disproved the Plum Pudding Model and showed that instead of a soup of positive charge, an atom consisted of a small nucleus of strong positive charge paving the way to Rutherford’s Atomic Model “ the atoms of the elements consist of a number of negatively electrified corpuscles enclosed in a sphere of uniform positive electrification, Philosophical Magazine, 1904 “… Thomson in Rutherford’s Atomic Model Rutherford-Geiger-Marsden Experiment Under supervision of Prof Rutherford ( student of Thomson) and scientist Geiger and graduate student Marsden, Thomson’s Plum Pudding Model was discarded by the Gold foil experiment in 1911 establishing Rutherford’s atomic model Quantum Number Summary – A set of quantum numbers describes a specific orbital • • • Energy and size - n Shape - l Orientation – ml 40 th Quantum Number! th A quantum number was added to describe the spin on a given electron – Called the electron spin quantum number - ms • Possible values: +1/2 and -1/2 41 More on electron spin • Each orbital can hold a maximum of electrons of opposite spin • Pauli exclusion principle states that no two electrons in an atom can have the same set of quantum numbers 42 Summary • Three quantum numbers describe a specific orbital – Energy and size, shape, and orientation • Four quantum numbers describe a specific electron in an atom 43 Stern-Gerlach Experiment Important in the field of quantum mechanics, the Stern–Gerlach experiment,after German physicists Otto Stern and Walther Gerlach, is a 1922 experiment on the deflection of particles, often used to illustrate basic principles of quantum mechanics It can be used to demonstrate that electrons and atoms have intrinsically quantum properties, and how measurement in quantum mechanics affects the system being measured The Stern–Gerlach experiment involves sending a beam of particles through an inhomogeneous magnetic field and observing their deflection The results show that particles possess an intrinsic angular momentum that is most closely analogous to the angular momentum of a classically spinning object, but that takes only certain quantized values (ie is not continuous) Aufbau Principle The Aufbau principle from the German Aufbau meaning "building up, construction": According to the principle, electrons fill orbitals starting at the lowest available (possible) energy states before filling higher states (e.g 1s before 2s) Pauli’s Exclusion Principle “No two electrons in a single atom can have the same four quantum numbers” Hund’s Rule If two or more orbitals of equal energy are available, electrons will occupy them singly before filling them in pairs Atoms at ground states tend to have as many unpaired electrons as possible Schrodinger’s Equation Schrodinger Equation gives the understanding of Quantum Mechanics Model: What did this equation for knowing more about atomic structure? Schroëdinger's equation eliminated the illogical quantum jump of electrons from one orbit to another as seen in Bohr’s Model, replacing it with a transitional process in which the wave pattern gradually fades out, while the new wave pattern fades in, during which time radiation is being emitted Schroëdinger equation can be used to predict and/or calculate the energy of atoms as electrons move around Wave function Ψ • A wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves Typically, its values are complex numbers and, for a single particle, it is a function of space and time Hamiltonian Operator • In quantum mechanics, the Hamiltonian is the operator corresponding to the total energy of the system It is usually denoted by H, also Ȟ or Ĥ Its spectrum is the set of possible outcomes when one measures the total energy of a system Because of its close relation to the time-evolution of a system, it is of fundamental importance in most formulations of quantum theory Particle in a 1-D Box An electron in a chemical bond is a real time example of a Particle in a 1-D box How is it so? Imagine an electron in a C-C single bond Since carbon atoms are roughly 24000 times more massive than an electron, thinking classically for a moment, this would be like a ball-bearing between two wrecking balls, which would certainly seem like two infinitely high walls The box length for a C-C single bond would be roughly 1.5 Å giving a defined confined space Uses: Particle in a 1-D box model can be used to predict the wavelength of maximum absorbance for highly conjugated organic molecules Particle in a 1-D box model has been used to predict energies of single bond systems Applications of Particle in a 1-D Box in Nanotechnology Energy Levels for 1-D Box: A Quantum Harmonic Oscillator Representing a ball on a spring in a classical harmonic oscillator, a quantum harmonic oscillator is applicable for vibrational motion of a diatomic molecule where, two atoms are assumed to be attached to a spring representing the chemical bond The energy solution is given by: The energy of a system described by a harmonic oscillator potential cannot have zero energy Thus, physical systems such as atoms in a solid lattice or in polyatomic molecules in a gas cannot have zero energy even at absolute zero temperature Example: Under atmospheric pressure liquid helium will not freeze at absolute zero temperature END OF MODULE [...]... continuous emission of energy by electron will ultimately lead to collapse of the atom Bohr corrected it by postulating that energy of an atom is quantized and can not take any continous values leading to Bohr’s atomic theory Black Body Radiation A black body is an ideal body which allows the whole of the incident radiation to pass into itself ( without reflecting the energy ) and absorbs within itself... states, it is accompanied by the emission or absorption of a photon.This photon's energy is given by Bohr’s Atomic Model ΔE=hf Rydberg’s Formula and Bohr’s Theory Rydberg’s formula is used to explain spectral lines of hydrogen like chemical elements Utilizing Bohr’s Postulates, it can be deduced that the energy of a photon emitted by a hydrogen atom is given by the difference of two hydrogen energy levels... whole number multiples of the constant, h Bohr’s Atomic Model Bohr’s Postulates 1 In an atom, the electrons revolve around the nucleus in certain definite circular paths called orbits, or shells 2 Each shell or orbit corresponds to a definite energy Therefore, these circular orbits are also known as energy levels or energy shells 3 Electrons in an atom can have only certain permissible energies 4...Rutherford’s Atomic Model Rutherford’s model based on Gold Leaf Experiment stated that the atom consists of a small, dense, positively charged core surrounded by negatively charged particles in a planetary model system Limitations of Rutherford’s Model The failure of Rutherford’s Model was in relation to Lamor’s Formula in classical physics which lead to the conclusion that continuous... Sommerfield’s Model also showed that orbits don’t have to lie on the same plane and could tilt in the presence of a magnetic field • The fundamental flaw was that orbitals could tilt relative to xy plane only in certain discrete values However, observation shows that an atom can be tilted w.r.t x,y,z co-ordinates without restriction This flaw is to be corrected by wave mechanics model of Schrodinger... objects emit more energy than colder λ (µm) objects F=σT 4 Applications of Black Body Radiation • Roughly we can say that the stars radiate like blackbody radiators This is important because it means that we can use the theory for blackbody radiators to infer things about stars like its effective temperature • Interesting applications include materials designing camouflage and radar absorbent Planck-Einstein... within itself this whole incident radiation (without passing on the energy) This propety is valid for radiation corresponding to all wavelengths and to all angels of incidence Therefore, the black body is an ideal absorber of incident radaition A body's behavior with regard to thermal radiation is characterized by its transmission τ, absorption α, and reflection ρ For a black body, τ=0, α=1, and ρ=0... astronomy because the Balmer lines appear in numerous stellar objects due to the abundance of hydrogen in the universe, and therefore are commonly seen and relatively strong compared to lines from other elements •The familiar red H-alpha spectral line of hydrogen gas in the far right, which is the transition from the shell n = 3 to the Balmer series shell n = 2, is one of the conspicuous colors of the... unit area) The amount of energy radiated is proportional to the temperature of the object 3) The hotter the object, the shorter the wavelength (λ) of emitted energy Ultraviolet (UV) Catastrophe The Rayleigh-Jeans Law: 2πckT I (λ , T ) = 4 λ * It agrees with experimental measurements for long wavelengths * It predicts an energy output that diverges towards infinity as wavelengths grow smaller * The failure... several convenient lines • Sommerfield proposed that not only do electrons travel in certain orbits but the orbits have different shapes and the orbits could tilt in the presence of a magnetic field Bohr’s Atomic Model This explained well the splitting of spectral lines observed for heavier elements Bohr-Sommerfield Model Advantages and Disadvantages of Bohr-Sommerfield Model • Sommerfield’s Model predicted ... matter Dalton assimilated the experimental works of many scientists to propose his ultimate modern theory of matter known as Dalton’s Atomic Theory Dalton’s Atomic Theory Dalton’s Atomic Theory... that atoms were considered to be fundamental particles that can not be cut or broken into parts The word “atom” was coined by him from the Greek adjective “atomos” meaning uncuttable Atomistic.. .Structure of the Atom Evolution of Atomic Theory First clear concept of Atom starts with the Jain School of Thought in th Century BC in India The Jains considered that matter is made of atoms