# QUANTUM THEORY AND ATOMIC STRUCTURE

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```					QUANTUM THEORY AND
ATOMIC STRUCTURE
The Nature of Light
 Visible light is one type of electromagnetic (EM)
and radiant energy. Other types include x-rays,
 All EM radiation consists of energy propagated
by means of electric and magnetic fields that
alternately increase and decrease in intensity as
they move through space
 This classical wave model distinguishes clearly
between waves and particles.
The Wave Nature of Light

c=νxλ
 Frequency (ν, greek nu) is the number of cycles
the wave undergoes per second, and is
expressed in units of 1/second (s-1 also called
hertz, Hz)
 Wavelength (λ, greek lambda) is the distance
between any point on a wave and the
corresponding point on the next wave; the
distance the wave travels during one cycle. It
expressed in meters and often in nanometers
(nm, 10-9 m) picometers (pm, 10-12 m)or
angstorm (, 10-10 m)
 Amplitude (intensity) of a wave is represented
by the height of the crest (or depth of the trough)
of the wave
The Electromagnetic Spectrum

The waves in the spectrum all travel at the same speed through a
vacuum but differ in frequency and therefore, wavelength
Sample Problem

A dental hygienist uses x-rays (λ = 1.00 )
to take a series of dental radiographs
while the patient listens to a radio station
(λ = 325 cm) and looks out the window at
the blue sky (λ = 473 nm). What is the
frequency (in s-1) of the electromagnetic
radiation from each source? Assume that
the radiation travels at the speed of light
3.00 x 108 m/s)
Solution

Converting from angstroms to meters
 = 1,00 Ǻ x 10-10 m/1 Ǻ = 1,00 x 10-10 m
 = c/ = 3,00 x 1018 s-1
Radio station :  = c/ = 9,23 x 107 s-1
Blue sky =  = c/ = 6,34 x 1014 s-1
The Distinction between Energy and Matter

Interference
troughs of interfering waves occur in the same positions
(waves are in phase )
•destructive interference: amplitudes cancel peaks of
one wave are in same position as troughs of the other
(waves are out of phase )
Diffraction                           Three ways to tell a wave from a particle

a wave can't bend around obstacles much larger than its
wavelength
what does this imply about the wavelength of sound waves?
waves are delocalized (spread out in space)
(1)        (2)        (3)
Waves can bend around small obstacle (1)
and fan out from pinholes (2) while
particles effuse from pinholes (3)
Interference
The Particle Nature of Light

The photoelectric effect
Atomic spectra
of Energy

A                                                               B
A. The interior of a cold ceramic-firing kiln approximates a blackbody, an object
that absorbs all radiation falling on it and appears black. A hot kiln emits light
characteristic of blackbody radiation. B Planck’s formula generates a curve that
fits perfectly the changes in energy and intensity of light emitted by blackbody
at different wavelength for a given temperature
Planck’s Formula
 To find a physical explanation of blackbody
glowing object could emit (or absorb) only
certain quantities of energy:
E = nh
 Where E is the energy of the radiation,  is its
frequency, n is a positive integer (1, 2, 3 and so
on) called a quantum number and h is a
proportionality constant now called Planck’s
constant and has value = 6,626x10-34 J.s
The Photoelectric Effect and The Photon
Theory of Light
 Current flow when monochromatic light
of sufficient energy shines on a metal
plate
 The photoelectric effect had certain
features: the presence of a threshold
frequency and the absence of a time
lag
 Carrying Planck’s idea of packeted
energy, Einstein proposed that light
itself is particulate, occurring as quanta
of electromagnetic energy, called
photon
 In terms of Planck’s work we can say
that each atom changes its energy
whenever it absorbs or emits one
photon, one “particle” of light, whose
energy is fixed by its frequency
 Ephoton = hν = ∆Eatom
Sampel Problem

A cook uses a microwave oven to heat a
meal. The wavelength of the radiation is
12,0 cm. what is the energy of one photon
Calculate the energies of one photon of
ultraviolet ( = 1x10-8 m), visible ( = 5x10-
7 m) and infrared ( = 1x10-4 m) light
Solution

E = h = hc/ = 1.66 x 10-24 J
UV: E = hc/ = 2x10-17 J
Visible: E = 4x10-19 m
IR: E = 2x10-21 m
Atomic Spectra
 Experimental key to atomic structure: analyze light
emitted by high temperature gaseous elements.
Experimental setup: spectroscopy

 Atoms emit a characteristic set of discrete wavelengths-
not a continuous spectrum!
atomic spectrum can be used as a "fingerprint" for an
element hypothesis: if atoms emit only discrete wavelengths,
maybe atoms can have only discrete energies an analogy
The Bohr Model of the Hydrogen Atom
 Soon after the nuclear model was proposed, Niels Bohr
suggested a model for the H atom that predicted the
existence of line spectra
 The H atom has only certain allowable energy levels called
stationary states
 The atom does not radiate energy while in one of its stationary
states
 The atom changes to another stationary state (the electron
moves to another orbit) only by absorbing or emitting a photon
whose energy equals the difference in energy between two
states:
 Ephoton = Estate A – E state B = hν
 where EA > EB . A spectral line results when a photon of
specific energy is emitted as the electron moves from a
higher energy state to a lower one.
The Wave-Particle Duality of Matter and
Energy
 Einstein proposed in his famous theory of
relativity that matter and energy are alternate
forms of the same entity
 This idea is embodied in his famous equation E
= mc2, which relates the quantity of energy
equivalent to a given mass and vice versa.
 This theory together with quantum theory have
completely blurred the sharp divisions between
matter (chunky and massive) and energy
(diffuse and massles) that we see around us
The Wave Nature of Electron and the
Particle Nature of Photon
 According to Bohr’s theory, an atom has only certain allowable
energy levels, however his assumption had no basis in physical
theory
 In 1920s de Broglie proposed if energy is particlelike perhaps matter
is wavelike. De Broglie reasoned that if electron have wavelike
motion and are restricted to orbits of fixed radii, that would explain
why they have only certain possible frequencies and energies
 Combining the equation the equation for mass-energy equivalence
(E = mc2) with that for energy of a photon (E = hν = hc/λ) de Broglie
derived an equation for the wavelength of any particle of mass m
moving at speed u
h

mu
 According to this equation, matter behaves as thought it moves in a
wave.
The de Broglie wavelengths of several
objects

Substance        Mass (g)     Speed (m/s)       (m)
Slow electron    9 x 10-28     1.0            7 x 10-4
Fast electron    9 x 10-28     5.9 x 106      1 x 10-10
Alpha particle   6,6 x 10-24   1.5 x 107      7 x 10-15
One-gram mass    1.0           0.01           7 x 10-29
Baseball         142           25.0           2 x 10-34
Earth            6.0 x 1027    3.0 x 104      4 x 10-63
Sample Problems

Calculate the de Broglie wavelength of an
electron with a speed of 1.00x106 m/s
(electron mass = 9.11x10-31 kg; h =
6.626x10-34 kg.m2/s)
What is the speed of an electron that has
a de Broglie wavelength of 100 nm?
Nugraha, 85 kg speed 30 km/jam

 = h/mu  7.27 x 10-10 m
u = h/m  7.27 x 103 m/s
The Quantum-Mechanical Model of the
Atom
Quantum Numbers of An Atomic Orbital

1. The principal quantum number (n) is a positive integer
(1, 2, 3 and so forth). It indicates the relative size of the
orbital and therefore the relative distance from the
nucleus of the peak in the radial probability distribution
plot
2. The angular momentum number (l) is an integer from 0
to n-1. it is related to the shape of the orbital and is
sometimes called orbital-shape quantum number
3. The magnetic quantum number (ml) is an integer from –l
through 0 to +l. it prescribes the orientation of the orbital
in the space around the nucleus and is sometimes
called the orbital-orientation quantum number
 The energy states and orbital of the atom are described
with specific terms and associated with one or more
quantum numbers:
 The atom’s energy levels or shells are given by n value;
the smaller the n value the lower the energy level and
the greater the probability of the electron being closer to
the nucleus
 The atom’s levels contain sublevels or subshells which
designate the orbital shape. Each sublevel has a letter
designation:
l = 0 is an s sublevel (sharp)
l = 1 is a p sublevel (principal)
l = 2 is a d sublevel (diffuse)
l = 3 is an f sublevel (fundamental)
 Each allowed combination of n, l and ml values specific
one of the atom’s orbital
Shape of
the s Orbital
The p Orbital
The d Orbital
One of the seven f orbital

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 views: 20 posted: 10/4/2012 language: English pages: 31