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PART 2 QUANTUM THEORY

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Quantum Mechanics Bohr’s theory can not explain spectra for atoms more complex than hydrogen, which show sub-lines In 1926 Erwin Schrodinger devised a theory to describe more complicated atoms: quantum mechanics This classifies regions of atoms into SHELLS, SUB-SHELLS and ORBITALS

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Quantum Theory Each electron in an atom is described by 4 different quantum numbers: n, l, ml, ms The first three (n, l and ml) describe an atomic orbital – a region of space where there is a probability of >90% of finding an electron They give the probability of finding an electron at various points in space (3 numbers because three dimensions) A fourth quantum number describes the spin of an electron

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**Quantum Numbers 1 and 2 SHELLS SUB-SHELLS**

1. PRINCIPAL QUANTUM NUMBER (n): one on which energy of an electron principally depends; orbitals with same n are in same shell; also determines size of an orbital; Values = 1, 2, 3,… SUB-SHELLS 2. ANGULAR MOMENTUM QUANTUM NUMBER (l): energy of an atom also depends to a small extent on l; distinguishes orbitals of same n by giving them different shapes; any integer value from 0 to n-1; orbitals of same n but different l are in different sub-shells: s p d f g Example: 2p indicates shell 2 (energy), sub-level p (shape)

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**Quantum Number 3 ORBITALS**

3. MAGNETIC QUANTUM NUMBER (ml): distinguishes orbitals in same shell and subshell (i.e. energy and shape) by giving them a different orientation in space; values = -l to +l

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s orbitals

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p orbitals

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d orbitals

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Summary of numbers 1-3 0 to n-1 -l to +l

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**Heisenberg’s Uncertainty Principle**

Werner Heisenberg stated in 1927 that it is impossible to know with precision both the position and the momentum of an electron The observer affects the observed Only noticeable on the sub-atomic scale (e.g. an electron, not a baseball, nor dust) It is not possible to define a point in space where an electron will be found However, we can obtain the probability of finding an electron at a certain point

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**Probability in a Hydrogen Atom**

An area where there is a greater than 90% chance of finding an electron = atomic orbital

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**n = 3 l = 0 l = 1 l = 2 -1 -2 +1 +2 3s 3p 3d n = 2 l = 0 l = 1 -1 +1**

-1 -2 +1 +2 3s 3p 3d n = 2 l = 0 l = 1 -1 +1 2s 2p SHELL n = 1 l = 0 1s SUB-SHELL ORBITAL

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**Pauli Exclusion Principle**

“No two electrons in any one atom can have the same four quantum numbers” An orbital can hold at most two electrons, and then only if the two electrons in that orbital have opposite spins

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Quantum Number 4 4. SPIN QUANTUM NUMBER (ms): each orbital can hold 2 electrons, and each has a different direction of spin, -½ and +½

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**18 8 2 l = 2 -2 -1 +1 +2 3d l = 1 -1 +1 3p n = 3 l = 0 3s l = 1 -1 +1**

+1 +2 3d l = 1 -1 +1 3p n = 3 18 l = 0 3s l = 1 -1 +1 2p n = 2 8 l = 0 2s SHELL n = 1 l = 0 1s 2 SUB-SHELL ORBITAL

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Hund’s Rule “Electrons fill each orbital singly with spins parallel before pairing occurs”

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**Electron configurations**

All of these ideas can be put together to start to write electronic configurations for atoms… Orbital notation: Spectroscopic notation: 1s2 2s2 2p1 Outer electrons, control chemical properties [He] 2s2 2p1

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Aufbau Principle Write the electron configuration (orbital and spectroscopic) for: helium, beryllium, oxygen, aluminium, calcium and bromine The Aufbau principle is a building up principle, which helps you to write electronic configurations “When electrons are placed in orbitals, the energy levels are filled up in order of increasing energy”

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Filling Orbitals 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f

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**Orbital energies Energy depends on n and l**

Different orbitals in the same subshell have the same energy Orbitals with the same energy are called degenerate There is interaction among different subshells in higher energy levels, which lowers their energy and explains the order of filling

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The Periodic Table p s d Grouped according to the last sub-shell being filled

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