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Lecture 12

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Quantum Model of the Atom

- Quantum Mechanics: The Wave Equation

ļ Schrodinger latched onto the idea of e- as waves and in 1925 came up with differential

equation (known as Schrodinger equation) to describe an e- in an atom as a wave

ļ Schrodinger Wave Equation (more detail)

ā Describes both the particle and wave nature of the e- in a hydrogen atoms

ļ Max Born realized that he can calculate the probability density for the e- by

looking at the function š2

o š2 gives a 3D probability density plot for an electronās position in space called

orbital

o We can calculate āshapesā that represent boundaries within which an electron

should be found

o Visual representation of the atom:

ļ Each electron is described by 3 quantum numbers: n for energy, ā for

angular momentum and m for spatial orientation

- Orbitals and Quantum Numbers

ļ© Atomic Orbital: a 3D description of the probability density for a given wave function

ļ© Orbital ā Orbit

ļ© Characterized by a set of quantum numbers which determine orbital size, energy, shape

and orientation

ļ© Principal Quantum Number, n

ļ Describes average size of the orbital and indicates the energy level

ļ n take on values of 1,2,3,4,5ā¦ (only positive integers)

ļ Numbers also correspond to letters where 1=K, 2=L, 3=M, 4=N, etcā¦

ļ In a hydrogen atom, the energy of an electron with principal quantum number n

is:

ļ ānā determines the size of this 90% boundary

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