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									                  Electron Energy Levels


Electron Shells


Ernest Rutherford's view of the atom consisted of a dense
nucleus surrounded by freely spinning electrons.
In 1913, the Danish physicist Niels Bohr proposed yet
another modification to the theory of atomic structure based
on a curious phenomenon called line spectra
When matter is heated, it gives off light.
For example, turning on an ordinary light bulb causes an
electric current to flow through a metal filament that heats the
filament and produces light. The electrical energy absorbed
by the filament excites the atoms' electrons, causing them to
"wiggle". This absorbed energy is eventually released from
the atoms in the form of light.
When normal white light, such as that from the sun,
is passed through a prism, the light separates into a
continuous spectrum of colors:
Bohr knew that when pure elements were excited by heat or
electricity, they gave off distinct colors rather than white light.
This phenomenon is most commonly seen in modern-day neon
lights, tubes filled with gaseous elements (most commonly
neon).
http://phet.colorado.edu/sims/fluorescent-lights/fluorescent-
lights.jnlp
When an electric current is passed through the gas, a
distinct color (most commonly red) is given off by the
element. When light from an excited element is passed
through a prism, only specific lines (or wavelengths) of
light can be seen. These lines of light are called line
spectra. For example, when hydrogen is heated and the
light is passed through a prism, the following line
spectra can be seen:
To Bohr, the line spectra phenomenon showed that atoms could
not emit energy continuously, but only in very precise
quantities (he described the energy emitted as quantized).
Because the emitted light was due to the movement of
electrons, Bohr suggested that electrons could not move
continuously in the atom (as Rutherford had suggested) but
only in precise steps. Bohr hypothesized that electrons occupy
specific energy levels. When an atom is excited, such as during
heating, electrons can jump to higher levels. When the electrons
fall back to lower energy levels, precise quanta of energy are
released as specific wavelengths (lines) of light.
                     Excitation
An atom gets to a higher energy state in a variety of ways
1 By collisions with other atoms
2 By collisions with an accelerated electron as in a discharge
tube where the electron is accelerated through the tube.When
the K.E of the electrons is equal to a change between the
energy levels in an atom in the tube then the energy may be
absorbed.
3 By the absorption of a phton of EM radiation with exactly
the correct quanta of energy.
Each level is given a number called the principal quantum
number of the electron in that state,with n = 1 representing the
electrons lowest possible energy its ground state.
The energy levels gradually increase to a value of ZERO.This
is equivalent to the ionisation of the atom and the electron
becomes free.
The levels have negative values because energy must be
supplied to eventually free and electron and ionise the atom.A
stationary free electron is considered to have zero energy hence
the energy levels must be negative to start with.
The ground state in hydrogen has n = 1 and an energy level of
13.6eV.
Under Bohr's theory, an electron's energy levels (also called
electron shells) can be imagined as concentric circles around
the nucleus. Normally, electrons exist in the ground state,
meaning they occupy the lowest energy level possible (the
electron shell closest to the nucleus). When an electron is
excited by adding energy to an atom (for example, when it is
heated), the electron will absorb energy, "jump" to a higher
energy level, and spin in the higher energy level. After a short
time, this electron will spontaneously "fall" back to a lower
energy level, giving off a quantum of light energy. Key to
Bohr's theory was the fact that the electron could only "jump"
and "fall" to precise energy levels, thus emitting a limited
spectrum of light. The animation linked below simulates this
process in a hydrogen atom
Visionlearning
ViewerBohr's theory of the hydrogen atom
                       Electron Energy Levels
Electrons can not have just any energy while orbiting the nucleus.
Only certain energy values are allowed.
Electrons may only gain or lose certain specific amounts of energy.

                                       Each element (atom and ion) has its
    When the electron is in a high energy shell, the atom is in an
                                       own distinctive set or pattern of energy
      excited state.                   levels - holds the key to studying of
    When the electron is in the lowest distant objects in the universe.
                                        energy shell, the atom is in the
       ground state.
                                       This diagram depicts the energy levels
                                       of Hydrogen.
                                       1 eV (electron volt) = 1.6 X 10-19 J

Electron jumps to higher energy levels can only occur with addition of the
particular amounts of energy representing differences between possible
energy levels. Energy levels are quantized - study of electron energy levels
called quantum mechanics. Atom gains this energy either from KE of another
atom colliding with it or from absorption of energy carried by light - falls to
lower energy level by emitting light or transfer of energy by collision.
The energies involved are so small that it makes sense to use
a more appropriate unit for energy than the Joule so we again
use the eV

 The energy carried by each photon is equal to the
 difference in energies between the two levels.

 This equation shows a transition between the
 levels n =2 and n = 1
 ΔE = E – E = hf =hc / λ
The spectrum of hydrogen is particularly important in
astronomy because most of the Universe is made of
hydrogen. Emission or absorption processes in hydrogen
give rise to series, which are sequences of lines
corresponding to atomic transitions, each ending or
beginning with the same atomic state in hydrogen. Thus,
for example, the Balmer Series involves transitions starting
(for absorption) or ending (for emission) with the first
excited state of hydrogen, while the Lyman Series involves
transitions that start or end with the ground state of
hydrogen;
This series of lines is called the Balmer series after
the discoverer J.J. Balmer
In the case of the Balmer series, each line
corresponds to an energy-level change which results
in the final energy state being n=2 ('second orbit‘
As expected, not all transitions end with n=2 ... some
end with n=1 ('first orbit'). These have very high
energies being so close to the nucleus (low orbits
have higher energies) and so photons emitted in
transitions to this final state are in the ultraviolet.
This is called the Lyman series of lines.
Other transitions end with n=3 and have lower
energy changes so photons emitted are in the infrared
(the Paschen series).
Absorption and Emission. When electrons jump from a low energy shell to a
high energy shell, they absorb energy. When electrons jump from a high
energy shell to a low energy shell, they emit energy. This energy is either
absorbed or emitted at very specific wavelengths, which are different for
each atom.
• There are 3 types of spectra:
• 1. Continuous spectrum 2.
  2.Absorption line spectrum
• dark lines in a continuous
  spectrum => light absorbed at
  certain wavelengths
• 3. Emission line spectrum
• bright lines at certain
  wavelengths (no continuous
  spectrum)
           Continuous Spectra



Contains all the possible wavelengths.
Spectrum of white light is continuous
                    Interaction of Light with Matter
                                                   So each electron is only
                                                   allowed to have certain
                                                   energies in an atom.
                                 Hydrogen          Electrons can absorb light
                                                   and gain energy or emit light
                                                   when they lose energy.
                                                   It is easiest to think of light
                                                   as a photon when
                   Emission Spectrum               discussing its interaction
                                                   with matter. Only photons
                                                   whose energies (colors)
                  Absorption Spectrum              match the “jump” in electron
                                                   energy levels can be emitted
                                                   or absorbed.

So visible emission spectrum is created when a gas is heated and collisions in
gas continually bump electrons to higher energy levels - emit photons of
specific wavelength as they fall back to lower levels. Absorption spectrum is
produced when white light is passed through cloud of cool gas. Photons of
specific wavelengths absorbed as electrons jump to higher energy levels.
Atomic Line Spectra
                        Absorption Spectra

             Spectroscopy and Atoms


                               Hydrogen




• If light shines through a cool gas, each element will absorb those
  photons whose colors match their electron energy levels.
• The resulting absorption line spectrum has all colors minus those
  that were absorbed.
• We can determine which elements are present in an object by
  identifying emission and absorption lines.
       Hot gases produce line emission spectra
If you heat up a gas to a high temperature many of its
elctrons become excited.They move up to a higher
energy level in their atoms.
As they fall back down to the ground state these
electrons emit energy in the form of photons.
If you split the light from a hot gas with a prism you
get a line spectrum.A line spectrum is seen as a series
of bright lines against a black background.
Each line corresponds to a particular wavelength of
light emitted by the source.Since only certain photon
energies are allowed for each element you can use the
spectrum of gas to tell what elements are in it.
The Hydrogen Atom. The hydrogen atom is the simplest of atoms. Its
nucleus contains only one proton which is orbited by only one electron.
In going from one allowed orbit to another, the electron absorbs or emits
light (photons) at very specific wavelengths. Note - wavelength is often
written as  and the unit used is an angstrom (A) = 10-8 m
 1 ångström = SI units 1×10−10 m
            = 0.1nm


Anders Jonas Ångström (August 13,
1814 – June 21, 1874) was a physicist
in Sweden, one of the founders of the
science of spectroscopy.


The Ångström crater on the Moon
was named in his honour.
Not only did Bohr predict that electrons would occupy specific
energy levels, he also predicted that those levels had limits to the
number of electrons each could hold. Under Bohr's theory, the
maximum capacity of the first (or innermost) electron shell is two
electrons. For any element with more than two electrons, the extra
electrons will reside in additional electron shells. For example, in
the ground state configuration of lithium (which has three
electrons) two electrons occupy the first shell and one electron
occupies the second shell. This is illustrated in the animation
linked below.
                         The Lithium atom
Atomic structure animation table
The Sun should produce pure white light i.e.
light from every frequency should be present. But
study the spectrum produced by the Sun and you
get gaps (lines) on it where light of particular
frequencies is missing.
Why? The light leaving the Sun has to pass
through gas clouds at the surface of the Sun. All
the photons of a particular frequency (and therefore
of a particular energy) are absorbed by the gas. In
fact, they are absorbed by electrons in the gas
atoms.
Why are only set frequencies absorbed? The reason
for this is that electrons can only exist in atoms in
certain energy states (or levels). Like books on a
bookshelf, you can’t have electrons half way between
one level and the next.
To move from one level to the next requires set
amounts of energy. Photons with these amounts of
energy are the ones absorbed by the gas. Other
photons, with more or less energy than these values,
are left untouched. Hence you get lines (which are
gaps) on the spectrum where photons are missing
To plot a path for something you need to know exactly where
the object is and be able to work out exactly where it's going
to be an instant later. You can't do this for electrons.
The Heisenberg Uncertainty Principle says - loosely - that
you can't know with certainty both where an electron is and
where it's going next. (What it actually says is that it is
impossible to define with absolute precision, at the same
time, both the position and the momentum of an electron.)
That makes it impossible to plot an orbit for an electron
around a nucleus. Is this a big problem? No. If something is
impossible, you have to accept it and find a way around it.
Suppose you had a single hydrogen atom and at a particular instant plotted
the position of the one electron. Soon afterwards, you do the same thing, and
find that it is in a new position. You have no idea how it got from the first place
to the second.
You keep on doing this over and over again, and gradually build up a sort of
3D map of the places that the electron is likely to be found.
In the hydrogen case, the electron can be found anywhere within a spherical
space surrounding the nucleus. The diagram shows a cross-section through
this spherical space.
95% of the time (or any other percentage you choose), the electron will be
found within a fairly easily defined region of space quite close to the nucleus.
Such a region of space is called an orbital. You can think of an orbital as
being the region of space in which the electron lives.
What is the electron doing in the orbital? We don't
know, we can't know, and so we just ignore the
problem! All you can say is that if an electron is in a
particular orbital it will have a particular definable
energy.
Each orbital has a name.
As a practical example consider first the alpha line for the
hydrogen atom (n=3 to n=2 transition). The upper level has n=3
but l=2 (and 2l+1 levels exist for m) so that possible states for this
level are 3S1/2,3P1/2, 3S3/2,3D3/2, and 3D5/2. In all the upper 'level' is
really FIVE separate levels!. The lower level with n=2 is also
composed of multiple hyperfine levels since l=1 and so m had 3
allowed levels. That 'level' is actually 2S1/2, 2P1/2, and 2P3/2. In all,
15 hyperfine transitions are possible. In reality, about 7 can be
resolved by high resolution spectroscopy. The situation is
complicated again when a larger atom is considered which has
multiple electrons in it's outer shell (which, of course, interact). In
the case of argon the inner 1S shell has 2 electrons, the next shells
are 2S with 2 electrons and 2P with 6. Finally the highest shell has
2 electrons in the 3S and 6 electrons in the 3P shells. When argon
becomes an ion, as it does in the argon ion laser, all sorts of
interactions occur in the outer shell!
RSS
http://www.slideshare.net/tufdaawg/models
              Useful links
• Emission Spectroscopy: Element
  identification
• A CD spectrometer
• Spectrometer - Wikipedia, the free
  encyclopedia
• Olympus Microscopy Resource Center:
  Physics of Light and Color - Particle and
  Wave Reflection: Interactive Java Tutorial
1.     The following is a simplified energy level
diagram for atomic hydrogen.
               0eV
          –0.850 e V
           –1.51 e V

           –3.40 e V




           –13.6 e V             Ground state
 State the ionisation energy of atomic hydrogen.
..............................................................................................................................................
..............................................................................................................................................
Account for the labelling of the energy levels with negative numbers.
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
                                                                                                                                                         (3)
            Calculate the wavelength of the photon emitted when an electron moves from the
–1.51 eV energy level to the –3.40 eV energy level.
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
                                                                                                        Wavelength = ........................................
                                                                                                                                                         (3)
Describe how you would produce a line spectrum of atomic hydrogen in a laboratory.
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
..............................................................................................................................................
                                                                                                                                                 (2)
Sketch what you would expect to see.
Ionisation energy of atomic hydrogen:
13.6 eV OR 2.18 × 10–18 J [– sign, X] (1)
                                                                                          1
Why energy levels are labelled with negative numbers:
          Work/energy is needed to raise the electrons/atoms to an energy of 0 eV, so
must start negative (1)(1)
OR
           Work/energy is given out when the electrons/atoms move to the ground
state, so energy now less than 0, i.e. negative   (1)(1)
OR
          the ground state is the most stable/lowest energy level of the
electrons/atoms and must be less than 0, i.e. negative       (1)(1)
                                                                                          2
         [1st mark essential: e– highest/maximum/surface/ionised/free has
energy = 0eV
          2nd mark: raising levels means energy in OR falling levels means energy out \
negative levels]
Wavelength of photon:
DE = 1.89 (eV)     (1)
Convert DE to joules, i.e. ×(1.6 × 10–19)
OR
 = [Their E]      (1)
= 6.6 × 10–7 (m) [6.5 – 6.7] (1)
                                                                           3
Production of line spectrum of atomic hydrogen in a laboratory:
          Source – hydrogen discharge tube/hydrogen lamp/low p hydrogen with
high V across      (1)
(view through) diffraction grating/prism/spectrometer/spectroscope   (1)
Einstein put forward a theory:
• Light energy is
  quantised.
• Light consists of a
  stream of particles
  called photons.
• The energy of each
  photon (E) depends       E=hf
   on the frequency (f )
  of the light.
The particle nature of waves
                 I suddenly got the idea,during
                the year 1923,that the discovery
                    made by Einstein in 1905
                    should be generalised by
                   extending it to all material
                 particles and notably electrons
                    Mass and speed
• One of the suprising consequences of Einsteins theory of relativity is
  that the mass of a moving object increases with speed.
• The mass of an object such as a proton and electron quoted in tables is
  its rest mass.At speeds up to about 0.2c the actual mass of a particle is
  very close to its rest mass.The particles observed mass increases very
   rapidly at speeds close to that of light.


  Relativity: Einstein's theory of relativity
  in animations and film clips. Einstein
  Light
           A bit of relativity
• The best known equation of all Physics is
  E = mc2
• A photon of Light has zero rest mass.But it
  has energy E and so from the above mass-
  energy relationship it must have an
  equivalent relativisitic mass given by the
  eqn m = E/c2
     Photons have momentum
• This means a photon has a momentum p

•     p = mc
•    but m = E/c2
• so p = (E/c2 ) x c
•         Giving p = E/c
          The Wave Nature of Particles

                                         hc
For instance, for a photon:   E  hf 
                                         
He suggested that a particle such of mass m moving with
velocity c (so its momentum is p = mc) may behave as a wave
with wavelength λ where

                                E hc h
                              p   
                                c c 
             An example
An electron is accelerated from rest through
a potential difference of 1000V may behave
as a particle.What is its wavelength?
K.E gained by electron = qV
so 1/2mv2 = qV
solving for v we get v = 1.8 x 107 ms-1
            λ= h/p
•           λ = h/mv
•   solving we get

•     λ = 4.0 x 10-11 ms-1
• often referred to as the De
  Broglie wavelength
     Problem: the wavelength of a
                proton
Calculate the de Broglie wavelength for a proton (mp=1.67x10-27 kg )
    moving with a speed of 1.00 x 107 m/s.
Calculate the de Broglie wavelength for a proton (mp=1.67x10-27 kg ) moving with a
    speed of 1.00 x 107 m/s.



                     Given the velocity and a mass of the proton we can
Given:               compute its wavelength

                                                h
v = 1.0 x 107m/s                          p 
                                               mpv

                     Or numerically,

Find:
                           ps 
                                            6.63 1034 J  s              3.97 1014 m
p = ?                             1.67 10   31
                                                       
                                                     kg 1.00 107 m s   
       The electron microscope
Just like other waves which can be diffracted
  this means that electrons and other particles
  can be diffracted.
 This was first observed to happen in 1925 by
 C.J.Davisson
            Diffraction
   the spreading of a wave around the
 edge of a barrier or through an opening

         Monochromatic light
   consists of only one color (wavelength).


          Polychromatic light
consists of more than one color (wavelength).
     Huygen’s Principle
  is used to explain diffraction.
“Each point on a wavefront acts
 as a new source of disturbance.”
             Click here to read about
                Christiaan Huygens.




Click here and here to view simulations
of Huygen’s Principle.

Huygen’s Principle can be used to explain
reflection and refraction, as shown here.
        Diffraction Gratings

  series of many slits etched on film

 Diffraction gratings (or replica gratings)
will separate light into its component colors
    through diffraction and interference.


  They are often used to identify the
component colors of polychromatic light.
Click here and here
to view simulations
of diffraction gratings.




Notice the changes in the diffraction
pattern as the variables are manipulated.
Young’s
Double Slit             = xd
Interference                L

                                     x
       d
                                     x
                         L
     is the wavelength of light
    d is the distance between slits
    x is the distance from the central bright band
      to the first order bright line
    L is the distance from slits to screen
Click here and
here to view
simulations
of double slit
interference.



Notice changes in the interference pattern
as each variable changes.
Click here,
here, here,
and here to
view single slit
interference
simulations.



Notice how the pattern changes as each
variable is manipulated.
              Characteristics
                 •central bright band
     •pattern spreads out as wavelength increases
  •pattern spreads out as distance to screen increases
•pattern spreads out as distance between slits decreases

 Similar results occur with a narrow single slit.
        Single Slit Interference
            Characteristics
                  •central bright band
       •narrower slit produces wider central band
         •larger wavelength gives wider pattern
       Thin Film Interference
 The color spectrum seen in a soap bubble, or
 any thin film, results from the interference
     of the reflections of light from the
     front and back surfaces of the film.




The colors seen depend on the thickness of the
 film. The light most strongly reflected has a
 wavelength such that the film thickness is an
  odd multiple of /4. Other wavelengths will
suffer partial or total destructive interference.
          Diffraction

Diffraction of water waves (opening)
 Diffraction is based on interference: a wave
 phenomenon
Diffraction: When light passes sharp edges or goes through narrow slits
the rays are deflected and produce fringers of light and dark bands.
                   Diffraction grating and helium-neon laser




   Light band    Constructive interference          +


   Dark band     Destructive interference           +
      Diffraction: example for x-rays and for electron
• In 1912 Max van Laue demonstrated diffraction of x-rays with a periodic
  crystal as a diffraction grating


      X-ray diffraction of the first
      man-made diamonds




• In 1927 Davisson and Germer confirmed the wave like nature of matter by
  showing that electron interacting with a periodic crystal also show diffraction


      Low energy electron diffraction (LEED)
      pattern from a clam GaN(0001)
             Diffraction Patterns

                                               The intensity pattern formed on
                                               a screen by diffraction from a
A double slit interference pattern of light.   square aperture




A double slit interference pattern of neurtons.
X-ray diffraction pattern for a single alum crystal.
• http://www.blacklightpower.com/FLASH/D
  oubleSlit_HighRes_Top.swf
• Science's 10 Most Beautiful Experiments
• http://mfile.akamai.com/7870/rm/mitstorage
  .download.akamai.com/7870/8/8.01/f99/vid
  eolectures/wl99lec34-300k.rm
           The Electron Microscope
• The electron microscope depends on the
  wave characteristics of electrons
• Microscopes can only resolve details
  that are slightly smaller than the
  wavelength of the radiation used to
  illuminate the object
• The electrons can be accelerated to high
  energies and have small wavelengths
     SUMMARY OF IMPORTANT EQUATIONS
                                          hc
• Energy and frequency:        E  h 
                                            


• The photoelectric effect:   KE  h  


                                h  h
• De Broglie wavelength:       
                                p mv


• Angular frequency:            2f
             Useful links
• WAVE PARTICLE DUALITY
• The Dual Nature of Light as Reflected in
  the Nobel Archives
• S-Cool! - AS & A2 Level Physics Revision
  Guide
• Topic 3 Particle Model of Light
             Albert Einstein 1879-1955
• We believe in the
  possibility of a theory
  which is able to give a
  complete description of
  reality, the laws of which
  establish relations between
  the things themselves and
  not merely between their
  probabilities ... GOD
  DOES NOT PLAY DICE.
              Niels Bohr 1885-1962

• Einstein, DON'T TELL
  GOD WHAT TO DO!

• Those who are not
  shocked when they first
  come across quantum
  mechanics cannot
  possibly have understood
  it.
         Werner Heisenberg 1901-1976
• We have to remember that
  what we observe is not
  nature itself but nature
  exposed to our method of
  questioning.

• I, at any rate, am
  convinced that HE IS
  NOT PLAYING AT
  DICE.
          Erwin Schroedinger 1887-1961

• I do not like it, and I am
  sorry I ever had anything
  to do with it.

• Had I known that we were
  not going to get rid of this
  damned quantum jumping,
  I never would have
  involved myself in this
  business!
              Prince Louis de Broglie
                    1892-1987
• Electrons should not be
  considered simply as
  particles, but that
  frequency must be
  assigned to them also.
  (1929, Nobel Prize Speech)
               Max Planck 1858-1947

• Physics is finished, young
  man. It's a dead-end street.

(from an unknown teacher to
         Planck considering
    Physics at the turn of the
                20th century!)
          Richard Feynman 1918-1988

• Anyone who has not
  been shocked by
  quantum physics has not
  understood it.

• The word 'quantum'
  refers to this peculiar
  aspect of nature that
  goes against common
  sense.
             Groucho Marx 1890-1977

• Very interesting theory - it
  makes no sense at all!

								
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