Calculate the Probability That a Transition Occurs from the Ground State - Download as DOC by fob12649


More Info
									                               Chapter 10- Modern Atomic Theory
                                         Rutherford’s Atom
The concept of a nuclear atom (charged electrons moving around the nucleus) resulted from Ernest
Rutherford’s experiments.
• Rutherford showed:
      – Atomic nucleus is composed of protons (positive) and neutrons (neutral).
      – The nucleus is very small compared to the size of the entire atom.
• Questions left unanswered:
      – How are elements arranged and how do they move?

Electromagnetic Radiation
   • Classical physics says matter made up of particles, energy travels in waves
   • Electromagnetic Radiation is radiant energy, both visible and invisible
   • Electromagnetic radiation travels in waves
   • Electromagnetic radiation given off by atoms when they have been excited by any form of energy
   • amplitude = A = measure of the intensity of the wave, “brightness”
   • wavelength =  = distance between two consecutive peaks or troughs in a wave
         – generally measured in nanometers (1 nm = 10-9 m)
   • frequency = = the number of waves that pass a point in space in one second
         – generally measured in Hertz (Hz),
         – 1 Hz = 1 wave/sec = 1 sec-1

Types of Electromagnetic Radiation

Planck’s Revelation
   • Showed that light energy could be thought of as particles for certain applications
   • Stated that light came in particles called quanta or photons
   • Particles of light have fixed amounts of energy

Basis of quantum theory
   • The energy of the photon is directly proportional to the frequency of light
                            Higher frequency = More energy in photons
   A photon of red light (relatively long wavelength) carries less energy than a photon of blue light
                                   (relatively short wavelength) does.

Problems with Rutherford’s Nuclear Model of the Atom
   • Electrons are moving charged particles
   • Moving charged particles give off energy
   • Therefore the atom should constantly be giving off energy
   • And the electrons should crash into the nucleus and the atom collapse!!

Emission of Energy by Atoms/Atomic Spectra
  • Atoms which have gained extra energy
      release that energy in the form of light
  • The light atoms give off or gain is of very
      specific wavelengths called a line spectrum
          – light given off = emission spectrum
          – light energy gained = absorption
          – extends to all regions of the
              electromagnetic spectrum
  • Each element has its own line spectrum which
      can be used to identify it

Atomic Spectra
   • The line spectrum must be related to energy transitions in the atom.
         – Absorption = atom gaining energy
         – Emission = atom releasing energy
   • Since all samples of an element give the exact same pattern of lines, every atom of that element must
      have only certain, identical energy states
   • The atom is quantized
         – If the atom could have all possible energies, then the result would be a continuous spectrum
             instead of lines
Bohr’s Model
• Explained spectra of hydrogen
• Energy of atom is related to the distance electron is
   from the nucleus
• Energy of the atom is quantized
        – atom can only have certain specific energy
           states called quantum levels or energy levels
        – when atom gains energy, electron “moves” to
           a higher quantum level
        – when atom loses energy, electron “moves” to
           a lower energy level
        – lines in spectrum correspond to the
           difference in energy between levels
• Atoms have a minimum energy called the ground
        – therefore they do not crash into the nucleus
• The ground state of hydrogen corresponds to having
   its one electron in an energy level that is closest to the nucleus
• Energy levels higher than the ground state are called excited states
        – the farther the energy level is from the nucleus, the higher its energy
• To put an electron in an excited state requires the addition of energy to the atom; bringing the electron
   back to the ground state releases energy in the form of light
• Distances between energy levels decreases as the energy increases
        – light given off in a transition from the second energy level to the first has a higher energy than
           light given off in a transition from the third to the second, etc.
        – Electrons “orbit” the nucleus much like planets orbiting the sun
• 1st energy level can hold 2e-1, the 2nd 8e-1, the 3rd 18e-1, etc.
        – farther from nucleus = more space = less repulsion
• The highest energy occupied ground state orbit is called the valence shell

Problems with the Bohr Model
   • Only explains hydrogen atom spectrum
         – and other 1 electron systems
   • Neglects interactions between electrons
   • Assumes circular or elliptical orbits for electrons - which is not true

Wave Mechanical Model of the Atom
  • Experiments later showed that electrons could be treated as waves
        – just as light energy could be treated as particles
  • The quantum mechanical model treats electrons as waves and uses wave mathematics to calculate
     probability densities of finding the electron in a particular region in the atom

   • Solutions to the wave equation give regions in space of high probability for finding the electron -
      these are called orbitals
          – usually use 90% probability to set the limit & are three-dimensional
   • Orbitals are defined by three integer terms called the quantum numbers
   • Each electron also has a FIFTH quantum number to represent the direction of spin
Orbitals and Energy Levels
• Principal energy levels identify how much
   energy the electrons in the orbital have
   – n
   – higher values mean orbital has higher
   – higher values mean orbital has farther
      average distance from the nucleus
• Each principal energy level contains one or
   more sublevels
   – there are n sublevels in each principal
      energy level
   – each type of sublevel has a different shape and energy
   – s<p<d<f
• Each sublevel contains one or more orbitals
   – s = 1 orbital, p = 3, d = 5, f = 7

Pauli Exclusion Principle
 • No orbital may have more than 2 electrons              •   p sublevel holds 6 electrons
 • Electrons in the same orbital must have                •   d sublevel holds 10 electrons
     opposite spins                                       •   f sublevel holds 14 electrons
 • s sublevel holds 2 electrons

Orbitals, Sublevels & Electrons
   • This is a list of the order in which electrons fill orbitals (by energy)
   • 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p
   • degenerate orbitals are orbitals with the same energy
           – each p sublevel has 3 degenerate p orbitals
           – each d sublevel has 5 degenerate d orbitals
           – each f sublevel has 7 degenerate f orbitals

                                                                  Hund’s Rule
                                                                    • for a set of degenerate orbitals,
                                                                        half fill each orbital first before
                                                                    • highest energy level called the
                                                                        valence shell
                                                                    – electrons in the valence shell
                                                                        called valence electrons
                                                                    – electrons not in the valence shell
                                                                        are called core electrons
                                                                    – often use symbol of previous
                                                                        noble gas to represent core
                                                                        electrons- 1s22s22p6 = [Ne]

Electron Configuration
   • Elements in the same column on the Periodic Table have
          – Similar chemical and physical properties
          – Similar valence shell electron configurations
                • Same numbers of valence electrons
                • Same orbital types
                • Different energy levels
Principle Components of the Wave Mechanical Model of the Atom!
   1. Atoms have a series of energy levels called principal energy levels, which are designated by whole
       numbers symbolized by n; n can equal 1,2,3,4,…. Level 1 corresponds to n = 1, level 2 corresponds
       to n=2, etc.

   2. The energy of the level increases as the value of n increases.

   3. Each principal energy level contains one or more types of orbitals called sublevels.

   4. The number of sublevels present in a given principal energy level equals n. Fore example, level q
      contains one sublevel (1s); level 2 contains two sublevels (2s & 2p – two types of orbitals), These are
      summarized in the following table. The number of each type of orbital is shown in parentheses.

          n                                Sublevels (Types of Orbitals) Present
          1                                                1s (1)
          2                                      2s (1)              2p (3)
          3                            3s (1)              3p (3)              3d (5)
          4                     4s (1)         4p (3)             4d (5)              4d (7)

   5. The n value is always used to label the orbitals of a given principal level and is followed by a letter
      that indicates the type (shape) of the orbital. For example, the designation 3p means an orbital in the
      3rd principal energy level that has two lobes (a p orbital always has two lobes)

   6. An orbital can be empty or it can contain one or two electrons, but never more than two. If two
      electrons occupy the same orbital, they must have opposite spins.

   7. The shape of an orbital does not indicate the details of electron movement. It indicates the
      probability distribution for an electron residing in that orbital.

Orbital Filling
   1. In a principal energy level that has d orbitals, the s orbital from the next level fills before the d
      oribitals in the current level. That is the (n + 1)s orbital always fills before the nd orbitals. For
      example, the 5s orbital will fill before the 4d orbital.

   2. After lanthanum, which has the electron configuration [Xe]6s25d1, a group of fourteen elements
      called the lanthanide series, or the lanthanides, occurs. This series of elements corresponds to the
      filling of the seven 4f orbitals.

   3. After actinium, which has the configuration [Rn]7s26d1, a group of fourteen elements called the
      actinide series, or the actinides, occurs. This series corresponds to the filling of the seven 5f orbitals.

   4. Except for helium, the group numbers indicate the sum of electrons in the ns and np orbitals in the
      highest principal energy level that contains electrons (where n is the number that indicates a
      particular principal energy level). These electrons are the valence electrons, the electron sin the
      outermost principal energy level of a given atom.
Good Test Questions:

How many more elements need to be discovered to get an electron into the 6f sublevel?

To top