Copulas From Infinitely Divisible Distributions-Applications to Credit Value at Risk
The Chemical Atom In the 5c BCE Democritus suggested that matter was not infinitely divisible but...
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The Chemical Atom
In the 5c BCE Democritus suggested that matter was not infinitely divisible but was made of small particles that could not be
cut - ATOMS.
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Plato 4c BCE
● Plato suggested that atoms of four Elements differed in shape
● Fire was a tetrahedron,air an octahedron, water an icosohedron and earth a cube.
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Daltons Atoms
● In 1812 John Dalton suggested that atoms were indestructible but combined together, in simple proportions, to make compounds.
● Atoms of different elements differed in mass.● He used assumptions about the formulas of
compounds ( assume 1:1 if no other evidence) to estimate relative atomic mass values.
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• So as 1g Hydrogen combine with 8g of Oxygen
• If the atoms are combined 1:1
• The oxygen atoms must be 8 time heavier than hydrogen atoms.
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19th century
19th Century chemists developed Daltons ideas.
Atoms were seen as assembled together in three dimensions to make the molecules of all the new substances discovered.
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Thompson's Atom 1890
● Thompson showed that small negative particles could be ejected from atoms.
● This led to the picture of the atom as a currant bun with electrons embedded in a positive matrix
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Rutherford 1910
● Used the experimental results of Geiger and Marsden.
● The mass of the atom is concentrated in a
small Nucleus.
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Niels Bohr 1915
• Electrons move in orbits around the nucleus.
• Only certain orbits are allowed.
• When an electron falls from a higher to a lower orbit the atom emits a photon of light.
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De Broglie 1924
• Developed Bohr’s ideas
• Allowed orbits have whole numbers of electron wavelengths
• So standing waves can exist.
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• If the orbit does not have a whole number of wavelengths it cannot exist.
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Schrodinger 1926
● Electrons exist in 3 D standing waves.
● Called Orbitals.● The square of the
amplitude is a measure of the probability of finding an electron at that point.
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The SHELL is indicated by the Principal Quantum Number n
As n increases the average distance of electrons in that shell from the nucleus increases.
n=1 n=2 n=3
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As n increases the number of types of orbital increases
for n=1 there is only one type of orbital (s)
For n = 2 , there are two types of orbital (s and p)s orbitals are spherical whilst p are dumbbell shaped
So for n=3 ?
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For n=3 as you decided there will be 3 types of orbital:
3s 3p 3d
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For n = 4 there will be
4
Types of orbitals
s p d f
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There is only one s orbital in each shell
There are 3 p orbitals in each shell at right angles to each other.
How many d orbitals are there ?
How many f orbitals ?
5
7