His theory assumed that e s acted as waves and not

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His theory assumed that e - ’s acted as waves and not particles. It was developed by analogy to classic equations for the motion of a guitar string (standing waves). Quantum mechanics is used to understand the structure of all atoms and molecules. The theory is very complicated, but the results are important.
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The square of the function, ψ 2 , gives the probability of finding an e - at a point. It is always positive. Quantum Model of the Atom Solutions of the wave equation wave equation are energies and mathematical functions. A ground-state probability map for the H-atom showing ψ 2 for each point in space. Bigger value = darker shade. The functions are called wave functions wave functions , ψ . They can be positive, negative or complex. Each ψ is identified by 3 quantum quantum numbers numbers .
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Beyond The Bohr Model: The QM Model of The Atom Line spectra for elements other than hydrogen had more lines ( Bohr model is simple ) De Broglie (1924) proposed electrons could have wave-like properties ( λ = h/mv ) Davisson & Germer (1927) observed electron diffraction pattern obtained for thin metal foil Electrons can be described by equations of waves Heisenberg’s ( 1932) uncertainty principle : it is impossible to simultaneously determine the exact position and the exact momentum of an electron. Inadequacy in the Bohr model Probability of finding an electron ( Schrodinger equation) – Wave equation & Wave functions ( complex mathematical equations)- orbital (quantum mechanical; not same as orbit)
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Quantum Mechanics Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated. It is known as quantum mechanics .
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Quantum Mechanics The wave equation is designated with a lower case Greek psi ( ψ ). The square of the wave equation, ψ 2 , gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.
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34 Schrodinger Wave Equation In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e - Wave function ( ψ ) describes: 1 . energy of e - with a given ψ 2 . probability of finding e - in a volume of space Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems.
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Quantum Numbers Solving the wave equation gives a set of wave functions, or orbitals , and their corresponding energies. Each orbital describes a spatial distribution of electron density. An orbital is described by a set of three quantum numbers .
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Quantum numbers (QN), energy levels & orbitals First quantum number, n : principal energy levels- n = 1,2,3,4… As n increases, the energy of the electron increases; is farther away from the nucleus ( not tightly bound to the nucleus). Second QN, l and subshells ( s,p.d,f ) Each principal energy level ( shell ) has subshells within it; n =1 , one subshell; others have > one; designated by second quantum number, l ( azimuthal QN) The shape of the orbital determined by the value of l l = 0,1, 2, 3….( n- 1) n =3; l = 0,1, or 2 ( three subshells ) n =4; l = 0, 1,2,3 (4 s , 4 p , 4 d , 4 f, four subshells)
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