Lecture 4 Notes 53750 - Lecture 4 Notes B. A. Rowland 53750...

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Lecture 4 Notes B. A. Rowland 53750 Hydrogen Orbitals The solutions for the Schrödinger equation for the hydrogen atom are characterized by four quantum numbers. n is called the principle quantum number . You may think of this quantity exactly as we thought about it in the particle in a box. n describes the energy and size of the orbital. Higher values of n represents higher energy levels of the hydrogen atom. As n increases the size of the orbital increases and the electron’s average distance from the nucleus also increases. Because n is restricted to integer values, the discrete nature of the hydrogen atom is explicitly in the orbital. The number of nodes in a hydrogen orbital is related to n via the expression: nodes = ( n – 1). l is called the angular momentum quantum number . l can take on any integer value from 0 to ( n – 1). This number describes the angular momentum of the electron in the hydrogen atom (think quantum rotation). l determines the shape of the orbital (spherical s ( l = 0), dumbbell shaped p ( l = 1), flower shaped d ( l = 2), f ( l = 3), g ( l = 4), etc). m l is known as the magnetic quantum number . m l can take on all integer values from – l to + l , including zero. m l describes the orientation of the orbital around the nucleus (i.e. is it oriented around the x-y, y-z, or x-z axes). It should be noted that for a hydrogen atom that, for a given principle number ( n ) the n s orbital will be equal in energy to the n p, n d, n f, etc. orbtials. This is called degeneracy . Probabilities and Orbitals We’ve discussed that we have to think in terms of probabilities now. The orbitals shown in the lecture slide actually represent the boundary at which you are 90% guaranteed to find the electron at any time. These are not orbits (due to the Uncertainty Principle)! s-orbitals s orbitals correspond to l = 0. Have nodes corresponding to ( n – 1). m l is equal to 0 for s orbitals. They are spherical in shape. Can only hold 2 electrons with opposite spin. Electrons in the s-orbital can penetrate to the nucleus of the atom (important for
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Lecture 4 Notes 53750 - Lecture 4 Notes B. A. Rowland 53750...

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