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Chapter 1 - Basic Concepts: atoms
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Charge Symbol Mass (kg)Charge Symbol Mass (kg) Mass (Amu) DiscoveryMass (Amu) Discovery
Proton +1 p+ 1.67310-27 1.00732 1919, Rutherford
Neutron 0 n0 1.67510-27 1.00870 1932, Chadwick
Electron -1 e- 9.11010-31 0.000549 1897, Thomson
Atomic and Mass Numbers
12
6C
SymbolMass number
Atomic number(optional)
Atomic number: equal to the number of protons in the
nucleus. All atoms of the same element have the samenumber of protons. Denoted by Z.
Mass number: equal to the sum of the number ofprotons and neutrons for an atom.
Atomic mass unit (amu) is 1/12 the mass of12C (1.660 10-27 kg)
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The atomic mass is the weighted average mass, of the naturally
occurring element. It is calculated from the isotopes of an element
weighted by their relative abundances.
atomic mass = fractionAmA + fractionBmB + . . .
Allotropes
element's atoms are bonded together in a different manner
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Successes in early quantum theory
==
22
'
111
nn
R
where R is theRydberg constant forH, 1.097105 cm-1
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=h
mv
where h is Plancksconstant,6.62610-34 Js
(x) (mv) h
4
Uncertainty Principle
Wave Nature of Matter
Schrdinger wave equation
The probability of finding an electron at a given point in space isdetermined from the function 2 where is the wavefunction.
0)(8
2
2
2
2
=+
VEh
m
dx
dwhere m = mass, E= totalenergy, and V= potentialenergy of the particle
1d
3d 0)(8
2
2
2
2
2
2
2
2
=+
+
+
VE
h
m
zyx
where m = mass, E= totalenergy, and V= potentialenergy of the particle
It is convenient to use spherical polar coordinates, withradial and angular parts of the wavefunction.
),()(),()(),,( ArRrzyx angularradialCartesian =
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Atomic Orbitals
A wavefunction is a mathematical function that contains detailedinformation about the behavior of an electron. An atomicwavefunction consists of a radial component R(r), and an angularcomponentA(,). The region of space defined by a wavefunction iscalled an atomic orbital.
Degenerate orbitals possess the same energy.
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-1122py
0122pz
+1122px
0022s
0011s
Angular part of
the wavefunction,
A(,)
Radial part of the
wavefunction,
R(r)
mllnAtomic
Orbital
re2
2/)2(22
1 rer
2/
62
1 rre
2/
62
1 rre
2/
62
1 rre
2
1
2
1
2
)cos(sin3
2
)(cos3
2
)sin(sin3
1s 2s
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ns orbitals have (n-1 radial nodes), np orbitals have (n-2 radial nodes),ndorbitals have (n-3 radial nodes), nforbitals have (n-4 radial nodes).
Radial Distribution Function,
4r2R(r)2
=1* d
=12 d
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Boundary surfaces for angular part of wavefunction, A(,)
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Orbitals energies in hydrogen-like species
2
2
nkZE = k = 1.312103 kJ mol-1
Z = atomic number
E
n =3
n =2
n =1
shell
3s
2s
1s
3p
2p
3d
In the absence of an electric or magnetic field these atomic orbitalenergy levels are degenerate; that is they are identical in energy.
Radial probability functions
Probability density
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Spin Quantum Number,Spin Quantum Number, mmss
Spin angular number, s,determines the magnitude of thespin angular momentum of aelectron and has a value of .
Since angular momentum is avector quantity, it must havedirection
Magnetic spin quantumnumber, ms, can have values+1/2 or -1/2.
An orbital is fully occupied when it contains two electrons which arespin paired; one electron has a value of ms = +1/2 and the other -1/2
ml= 2 +2(h/2)
ml= 1 +(h/2)
ml= 0 0
ml = -1 -(h/2
)
)2/(6 h
)2/(6 h
)2/(6 h
)2/(6 h
)2/(6 hm
l= -2 -2(h/2)
Resultantangularmomentum
Resultantmagnetic
moment
Angular momentum, the inner quantum number, j, spin-orbit coupling
z component of orbitalangular momentum
orbital angularmomentum
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1H ground state Many-electron atom
Ground State Electronic ConfigurationsGround State Electronic Configurations
Some irregularities: seeTable 1.3 in textbook
The sequence thatapproximately describesthe relative energies ororbitals in neu t r a l atoms:
1s < 2s < 2p < 3s < 3p