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)
  radiation, also called electromagnetic energy
  and radiant energy. Other types include x-rays,
  microwaves and radio waves
 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
    •constructive interference: amplitudes add peaks,
    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?
radio waves? visible light?
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

Blackbody radiation
The photoelectric effect
Atomic spectra
Blackbody Radiation and the Quantization
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
  Planck made a radical assumption that the hot,
  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
 of this microwave radiation?
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
Answer

 = 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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