Title: Electronic Structure of Atoms
1Electronic Structure of Atoms Wave nature of
matter In 1925 Louis de Broglie proposed that
matter has wave properties mv is mass x
velocity momentum Examples what is the
wavelength of an electron with velocity 5x106
m/s? What is the wavelength of a baseball
(0.1415 kg) with velocity 1500 m/s? In 1927,
Davisson and Germer showed that high speed
electrons are diffracted by crystals just like
x-rays The electron microscope is a application
of the wave nature of high speed electrons used
to image matter with great magnification.
2- Electron Structure of Atoms
- Heisenberg Uncertainty Principle states that it
is impossible to know exactly both the position
and momentum of an object. - The uncertainty principle implies a probabilistic
view of nature and has important consequences
regarding our viewpoint of how the electron
behaves in the atom. - If one knows exactly the velocity of the electron
one cannot know its position - Velocity refers both to speed - Dx/Dt - and
direction of travel - Schrödingers Wave Mechanics views the electron
as a standing wave inside an atom - There are two important results from this picture
of how the electron behaves in the atom - Wave mechanics gives the energies of the electron
waves - Wave mechanics gives the three dimensional shapes
of the electron waves in a probability density
picture.
3- Electron Structure of Atoms
- The results of wave mechanics are expressed in
the form of a wave function, Y. Y characterizes
the electron as a matter wave - The behavior of the electron in an atom is best
described as a standing wave where only certain
wave functions are possible - Each wave function corresponds to an allowed
energy value for the electron - A natural consequence of the wave mechanics is
the energy of an electron is quantized - Y2 gives information on the probability density
- the probability of finding the electron within
a given region of space - This is often referred to as the electron density
in a given region of space - Each of the Ys are called orbitals
- Each orbital is described in terms of 3 quantum
numbers
4- Electronic Structure of Atoms
- Quantum numbers
- n is called the principal quantum number and has
integer value 1, 2, 3, - The greater n, the greater the average distance
or most probable distance for finding the
electron wave from the nucleus. - The energy of an electron with a particular n
value is the same as calculated from the Bohr
model En -Rhc/n2 - Each n value represents an electron shell. A
shell may contain more than 1 e. - l is called the angular momentum or azimuthal
quantum number and has integer values of - 0, 1, 2, , n-1.
- The value of this quantum number is associated
with the shape of the orbital - lower case letters are applied to these quantum
numbers - 0s 1p 2d 3f 4g
- ml is called the magnetic quantum number and it
describes the orientation of the orbital in
space and has values - - l , - l 1, , 0, 1, 2, , l
5- Electron Structure of Atoms
- Quantum Numbers and Orbitals
- A shell is the collection of orbitals with the
same n value - A subshell is the collection of orbitals having
the same n and l value - The restriction of the values of the quantum
numbers indicates how many orbitals are in each
shell or subshell. - Each shell with a value of n consists of n
subshells - There are n values of l for n1, there is only
one value of l 0 for n2 there are 2 values for
l0,1 for n3, there are 3 values of l0,1,2. - Each subshell has 2 l1 orbitals corresponding to
the 2 l1 values of ml - An s subshell (l 0) has one orbital there is
only one value for ml . - A p subshell (l 1) has 3 orbitals there are 3
values for ml . - There are n2 orbitals in a shell. This is
important in explaining the organization of the
periodic table into rows of various lengths.
6- Electronic Structure of Atoms
- H Atom Orbital shapes see Kotz Treichel, p
319-323. - Three Dimensional Shapes of Orbitals
- s oritals are spherically symmetric
- As n gets larger, the electron probability
increases at larger distances from the nucleus. - There are n- l -1 nodes for s orbitals these are
radial nodes. - p orbitals have two lobes separated by a planar
node - There are n- l -1 radial nodes and l 1 planar
nodes - d orbitals have four lobes separated by two
planar nodes - There are n- l -1 radial nodes and l 2 nodal
planes - Often a contour representation is more than
adequate to show the shape of an orbital - This shows an outer boundary inside which is
found the major probability of finding the
electron
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8Boundary surface diagrams for electron densities
of 1s, 2s, 3s, 2p, 3p, and 3d orbitals. Note s
orbitals have no nodal planes, p orbitals have 1
nodal plane and d orbitals have 2 nodal planes
9Nodal planes for p and d orbitals
10Plots of y2 vs. distance from the nucleus for 1s,
2s, and 3s orbitals of the H atom. Points where
y2 0 define the radii of spherical nodes
11Plot of Y vs. distance from the nucleus of a 2p
orbital for an H atom along the axis of maximum
electron density.
12- Electronic Structure of Atoms
- Magnetism is a phenomenon associated with the
motion of electric charge in matter - It is most often associated with the interaction
of compass needles with the earths magnetic
field or the attraction of iron containing
objects by bar magnets - If electric charge moves in matter, the matter
will have magnet properties - Most matter is diamagnetic and is repelled by a
magnet - Some substances are attracted to a magnet and are
paramagnetic or ferromagnetic - Paramagnetism and ferromagnetism result from a
property of the electron called electron spin
13- Electronic Structure of Atoms
- Electron Spin
- The electron behaves like a spinning charge and
has an associated magnetic moment that causes
it to act like a bar magnet - Electron spin is quantized and has quantum number
ms 1 or -1 - An atom like H with one electron is
paramagnetic, whereas He is diamagnetic - It appears that the one electron in Hs 1s
orbital confers the paramagnetism - The second electron in Hes 1s orbital must be
of opposite spin and the net result is a
cancellation of the magnetism of each electron - The electrons are said to be paired or spin paired
14- Electronic Structure of Atoms
- The Pauli Exclusion Principle states that no two
electrons in an atom may have the same values
for all four quantum numbers. - The n, l and ml values define the orbitals in
an atoms and since there are only two values for
ms, each orbital can have only 2 electrons in it. - Orbital box diagrams make use of a box
representing each orbital - Electrons are represented as either an
up-pointing arrow (ms ) or down-pointing
arrow (ms - ) - For H atom
N1, 0, ml0, ms
1s or
N1, 0, ml0, ms -
1s
N1, 0, ml0, ms
N1, 0, ml0, ms -
1s
15Number of electrons accommodated in by shell and
subshell with n 1 to 6