#### Transcript ATOMIC STRUCTURE Chapter 7

```ATOMIC STRUCTURE
Kotz Ch 7 & Ch 22 (sect 4,5)
• properties of light
• spectroscopy
• quantum hypothesis
• hydrogen atom
• Heisenberg
Uncertainty Principle
• orbitals
• subatomic particles (electron, photon, etc)
have both PARTICLE and WAVE properties
• Light is electromagnetic radiation crossed electric and magnetic waves:
Properties :
Wavelength, l (nm)
Frequency, n (s-1, Hz)
Amplitude, A
constant speed. c
3.00 x 108 m.s-1
wavelength
Visible light
Amplitude
wavelength
Node
• All waves have:
frequency
and
wavelength
• symbol: n (Greek letter “nu”)
l (Greek “lambda”)
• units:
“distance” (nm)
“cycles per sec” = Hertz
l•n = c
where c = velocity of light = 3.00 x 108 m/sec
Note: Long wavelength
 small frequency
Short wavelength
 high frequency
increasing
frequency
increasing
wavelength
Example: Red light has l = 700 nm.
Calculate the frequency,
c
=
n=
l
3.00 x 108 m/s
7.00 x 10-7 m
n.
= 4.29 x 1014 Hz
• Wave nature of light is shown by classical
wave properties such as
• interference
• diffraction
Quantization of Energy
Max Planck (1858-1947)
Solved the “ultraviolet
catastrophe”
4-HOT_BAR.MOV
• Planck’s hypothesis: An object can only
gain or lose energy by absorbing or
Quantization of Energy (2)
Energy of radiation is proportional to frequency.
E = h•n
where h = Planck’s constant = 6.6262 x 10-34 J•s
Light with large l (small n) has a small E.
Light with a short l (large n) has a large E.
Photoelectric Effect
Albert Einstein (1879-1955)
Photoelectric effect demonstrates the
particle nature of light. (Kotz, figure 7.6)
No e- observed until light
of a certain minimum E is used.
Number of e- ejected does NOT
depend on frequency, rather it
depends on light intensity.
Photoelectric Effect (2)
• Classical theory said that E of ejected
electron should increase with increase
in light intensity — not observed!
• Experimental observations can be
explained if light consists of
particles called PHOTONS of
discrete energy.
PROBLEM: Calculate the energy of
1.00 mol of photons of red light.
l = 700 nm n = 4.29 x 1014 sec-1
E = h•n
= (6.63 x 10-34 J•s)(4.29 x 1014 sec-1)
= 2.85 x 10-19 J per photon
E per mol = (2.85 x 10-19 J/ph)(6.02 x 1023 ph/mol)
= 171.6 kJ/mol
- the range of energies that can break bonds.
Atomic Line Spectra
• Bohr’s greatest contribution to
science was in building a
simple model of the atom.
• It was based on understanding
the SHARP LINE SPECTRA
of excited atoms.
Niels Bohr (1885-1962)
(Nobel Prize, 1922)
Line Spectra of Excited Atoms
• Excited atoms emit light of only certain wavelengths
• The wavelengths of emitted light depend on the
element.
H
Hg
Ne
Atomic Spectra and Bohr Model
One view of atomic structure in early 20th
century was that an electron (e-) traveled
about the nucleus in an orbit.
+
Electron
orbit
1. Classically any orbit should be
possible and so is any energy.
2. But a charged particle moving in an
electric field should emit energy.
End result should be destruction!
Atomic Spectra and Bohr Model (2)
• Bohr said classical view is wrong.
• Need a new theory — now called QUANTUM
or WAVE MECHANICS.
• e- can only exist in certain discrete orbits
— called stationary states.
• e- is restricted to QUANTIZED energy states.
Energy of state = - C/n2
where
C is a CONSTANT
n = QUANTUM NUMBER, n = 1, 2, 3, 4, ....
Atomic Spectra and Bohr Model (3)
Energy of quantized state = - C/n2
• Only orbits where n = integral
number are permitted.
= n2 x (0.0529 nm)
• Results can be used to
explain atomic spectra.
Atomic Spectra and Bohr Model (4)
If e-’s are in quantized energy
states, then DE of states can
have only certain values. This
explains sharp line spectra.
E = -C
(1/22)
H atom
n=2
07m07an1.mov
E = -C (1/12)
n=1
4-H_SPECTRA.MOV
Calculate DE for e- in H “falling” from
n = 2 to n = 1 (higher to lower energy) .
Energy
Atomic Spectra and Bohr Model (5)
n=2
n=1
DE = Efinal - Einitial = -C[(1/12) - (1/2)2] = -(3/4)C
• (-ve sign for DE indicates emission (+ve for absorption)
• since energy (wavelength, frequency) of light can only be +ve
it is best to consider such calculations as DE = Eupper - Elower
C has been found from experiment. It is now called R,
the Rydberg constant. R = 1312 kJ/mol or 3.29 x 1015 Hz
so, E of emitted light = (3/4)R = 2.47 x 1015 Hz
and l = c/n = 121.6 nm (in ULTRAVIOLET region)
This is exactly in agreement with experiment!
Hydrogen atom spectra
High E
Short l
High n
Low E
Long l
Low n
Visible lines in H atom
spectrum are called the
BALMER series.
6
5
4
Energy
3
2
1
En = -1312
n2
Ultra Violet
Lyman
Visible
Balmer
Infrared
Paschen
n
From Bohr model to Quantum mechanics
Bohr’s theory was a great accomplishment
and radically changed our view of matter.
But problems existed with Bohr theory —
– theory only successful for the H atom.
– introduced quantum idea artificially.
• So, we go on to QUANTUM or WAVE
MECHANICS
Quantum or Wave Mechanics
• Light has both wave & particle
properties
• de Broglie (1924) proposed that all
moving objects have wave
properties.
• For light: E = hn = hc / l
L. de Broglie
(1892-1987)
• For particles: E = mc2
Therefore, mc = h / l
(Einstein)
and for particles
(mass)x(velocity) = h / l
l for particles is called the de Broglie wavelength
WAVE properties of matter
Electron diffraction with
electrons of 5-200 keV
- Fig. 7.14 - Al metal
Davisson & Germer 1927
Na Atom Laser beams
l = 15 micometers (mm)
Andrews, Mewes, Ketterle
M.I.T. Nov 1996
The new atom laser emits pulses of coherent atoms,
or atoms that "march in lock-step." Each pulse
contains several million coherent atoms and
is accelerated downward by gravity. The curved
shape of the pulses was caused by gravity and forces
between the atoms. (Field of view 2.5 mm X 5.0 mm.)
4-ATOMLSR.MOV
Quantum or Wave Mechanics
Schrodinger applied idea of ebehaving as a wave to the
problem of electrons in atoms.
Solution to WAVE EQUATION
gives set of mathematical
expressions called
E. Schrodinger
1887-1961
WAVE FUNCTIONS, Y
Each describes an allowed energy
state of an eQuantization introduced naturally.
WAVE FUNCTIONS, Y
• Y is a function of distance and two
angles.
• For 1 electron, Y corresponds to an
ORBITAL — the region of space
•
•
within which an electron is found.
Y does NOT describe the exact
location of the electron.
Y2 is proportional to the probability of
finding an e- at a given point.
Uncertainty Principle
W. Heisenberg
1901-1976
Problem of defining nature of
electrons in atoms solved by
W. Heisenberg.
Cannot simultaneously define
the position and momentum
(= m•v) of an electron.
Dx. Dp = h
At best we can describe the
position and velocity of an
electron by a
PROBABILITY DISTRIBUTION,
2
which is given by Y
Wavefunctions (3)
Y2 is proportional to the probability
of finding an e- at a given point.
4-S_ORBITAL.MOV
(07m13an1.mov)
Orbital Quantum Numbers
An atomic orbital is defined by 3 quantum
numbers:
– n l ml
Electrons are arranged in shells and
subshells of ORBITALS .
n  shell
l
 subshell
ml  designates an orbital within a subshell
Quantum Numbers
Symbol
Values
Description
n (major)
1, 2, 3, ..
Orbital size and
energy = -R(1/n2)
l (angular)
0, 1, 2, .. n-1
Orbital shape or
type (subshell)
ml (magnetic)
-l..0..+l
Orbital orientation
in space
Total # of orbitals in lth subshell = 2 l + 1
Shells and Subshells
For n = 1, l = 0 and ml = 0
There is only one subshell and that
subshell has a single orbital
(ml has a single value ---> 1 orbital)
This subshell is labeled s (“ess”) and
we call this orbital 1s
Each shell has 1 orbital labeled s.
It is SPHERICAL in shape.
s Orbitals
All s orbitals are spherical in shape.
p Orbitals
For n = 2, l = 0 and 1
There are 2 types of
orbitals — 2 subshells
For l = 0 ml = 0
this is a s subshell
For l = 1 ml = -1, 0, +1
this is a p subshell
with 3 orbitals
Typical p orbital
planar node
When l = 1, there is
a PLANAR NODE
through the
nucleus.
p orbitals (2)
pz
90 o
A p orbital
px
py
The three p
orbitals lie 90o
apart in space
l=
px
py
pz
p-orbitals(3)
n=
2
3
d Orbitals
For n = 3, what are the values of l?
l = 0, 1, 2
and so there are 3 subshells in the shell.
For l = 0, ml = 0
 s subshell with single orbital
For l = 1, ml = -1, 0, +1

p subshell with 3 orbitals
For l = 2, ml = -2, -1, 0, +1, +2
 d subshell with 5 orbitals
d Orbitals
typical d orbital
s orbitals have no planar
node (l = 0) and
so are spherical.
planar node
p orbitals have l = 1, and
planar node
have 1 planar node,
and so are “dumbbell”
IN GENERAL
shaped.
the number of NODES
d orbitals (with l = 2)
= value of angular
have 2 planar nodes
quantum number (l)
Boundary surfaces for all orbitals of the
n = 1, n = 2 and n = 3 shells
n=
3d
3
2
There are
n2
orbitals in
the nth SHELL
1
ATOMIC ELECTRON
CONFIGURATIONS AND PERIODICITY
Element Mnemonic Competition
Hey! Here Lies Ben Brown. Could Not Order Fire. Near
Nancy Margaret Alice Sits Peggy Sucking Clorets. Are
Kids Capable ?
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