Chapter 11 – Modern Atomic Theory

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World of Chemistry Notes for Students                                            [Chapter 11, page 1]

                             Chapter 11  Modern Atomic Theory

0) This chapter is a continuation of our discussions from Chapter 3 during which we saw how
   atoms, electrons, protons, and neutrons were discovered. I am going to assume that you
   remember Dalton, J. J. Thomson, Lord Kelvin, Roentgen, and Rutherford from that chapter.

    This chapter will bring us from the early 1900's to current times in looking at the atom and
    atomic structure.

1) Sec 11.1  Rutherford's Atom
   1) An atom contains a nucleus which has a very small volume compared to the volume of the
       atom, but almost all of the mass of the atom is in the nucleus. The nucleus contains the
       protons (+1 charge, mass = 1.0 amu) and neutrons (no charge, mass = 1.0 amu).
       Electrons have -1 charge, 0.00055 amu.

        Atomic Number = # of protons        Mass Number = # of protons + # of neutrons

    2) The number of electrons in a neutral atom is the same as the number of protons.

    3) Rutherford thought that the electrons might move around the nucleus somewhat like the
       planets move around our sun, but he could not explain how this happened nor why the
       electrons were not drawn into the nucleus.

2) Sec 11.2  Energy and Light

    The work that led to the development of the modern model of the atom grew out of the study
    of light. Remember that the people who discovered the protons, neutrons and electrons began
    by studying electricity and energy. Light is only a small part of the entire thing that is called
    electromagnetic energy or radiation.

    a) Electromagnetic Energy (Light waves) is the energy carried through space by means of
       wavelike oscillations. The oscillations are systematic fluctuations in the intensities of very
       tiny electrical and magnetic forces. Electromagnetic radiation has a wavelength (lambda,
       8) and a velocity (c) which is 3.0 x 108 m/sec. The frequency (nu, <) refers to the number
       of waves that pass a given point in a certain amount of time. The unit of frequency is the
       Hertz (Hz = cycles/sec). We can relate these things in the following experssion:

                        < = c = m/sec =           1 ; therefore Hertz = s-1 = Hz
                            l    m                s

    b) Visible light covers a small part of the total spectrum. For most people, light is visible if it
       has a wavelength between 400 nm (violet) and 750 nm (red).
                        1 A = 1 x 10-10 m                       1 nm = 1 x 10-9 m

                                             The Spectrum

gamma rays       x-rays        ultra-violet         visible       infra-red     microwave       radio
<------------|-------------|--------------------|--------------|--------------|--------------|--------->
                                             400 nm          750 nm
       shorter wavelength                                                  longer wavelength
       long frequency                                                      small frequency
World of Chemistry Notes for Students                                         [Chapter 11, page 2]

   Examples
   1) What is the frequency in hertz of violet light?




   2) What is the wavelength of radio waves that have a frequency of 1240 kHz?




   c) Often we can look at the energy that is involved with all of these as packets of energy,
      distinct units, which are often called photons.

       What is the exact nature of light? Does it consist of waves or is it a stream of particles? It
       seems to be both. This leads to what is called the wave-particle duality of the nature of
       light.


3) Sec 11.3  Emission of Energy by Atoms
   When energy (heat, electrical, or light) is added to a substance, some or all of the energy may
   be absorbed by the substance which then exists in an excited state. The substance will later
   become unexcited by losing the energy as a photon of light, which can be observed by a
   spectroscope.

                       ' Excited atom
                                                                              Photon of
                                                                              light
       Energy                                                                 emitted

                                                               Lower energy state


   High-energy photons correspond to short-wavelength light and low-energy photons correspond
   to long-wavelength light.




   Atomic Spectra  We refer to this in terms of atomic spectra  literally, the light from atoms.

       1) Continuous Spectrum  A spectrum that contains all wavelengths of visible light. When
          sunlight is passed through a prism, the light is separated into a spectrum.

       2) Atomic Emission Spectra  The light emitted by elements consists of sharp lines in the
          visible or near U.V. part of the spectrum.

   DEMONSTRATION  Observation of Atomic Emission Spectrum of Selected Elements.
World of Chemistry Notes for Students                                         [Chapter 11, page 3]

4) Sec 11.4  The Energy levels of Hydrogen

    The hydrogen atom is the simplest system we can look at because it only has one electron to
    consider. When a hydrogen atom absorbs energy from some outside source, it uses this energy
    to go to a higher or excited energy state. It can release this excess energy (go to a lower
    energy state) by emitting a photon of light.

    The important thing here is to recognize that the energy contained in the photon corresponds
    to the change in energy that the atom experiences in going from the excited to the lower
    energy state.

    What we also see, however, is that only certain photons of visible light are emitted. We might
    have assumed that all wavelengths of light would appear. We do not see all colors.

                                        Hydrogen Spectrum




        Atomic Emission Spectrum of Hydrogen  Consists of 4 lines in the visible region of the
        spectrum (410 nm, 434 nm, 486 nm, 656 nm).

        These results tell us that only certain photons are emitted which means that only certain
        energy changes are occurring. This means that the hydrogen electron can only have certain
        discrete energy levels. The same colors are always emitted with hydrogen, so we must
        assume that all hydrogen atoms have the same set of discrete energy levels. This was a
        change because people expected that atoms could have a continuous set of energy levels
        rather than only certain values. This discovery greatly changed how people looked at the
        atom.

5) Sec 11.5  The Bohr Model of the Atom

    In 1913 Niels Bohr proposed that electrons are arranged in concentric circular paths, or orbits,
    around the nucleus (sometimes referred to as the planetary model). He proposed that electrons
    in a particular path have a fixed energy. To move from one energy level (orbit) to another, an
    electron must gain or lose just the right amount of energy. The energy levels in an atom are
    not equally spaced. They move closer together as we move to higher energy levels. A
    quantum is the amount of energy required to move an electron from its present energy level to
    the next higher one. Thus, the energy of the electron is said to be quantized.

    Bohr's model gave an excellent explanation of the spectrum of the hydrogen atom but did not
    work at all with atoms containing more than one electron. However, the ideas of quantum
    numbers and fixed energy levels were useful in later theories.

6) Sec 11.6  The Wave (or Quantum) Mechanical Model of the Atom
   The modern description of the electrons in atoms derives from the solution to the Schroedinger
   Equation. This model is primarily mathematical. It has few, if any, analogies in the visible world.
World of Chemistry Notes for Students                                          [Chapter 11, page 4]

   It takes into consideration the possibility that an electron can behave like a wave and not just a
   particle.

   Like the Bohr model, the quantum mechanical model of the atom leads to fixed energy levels for
   an atom.

   Unlike the Bohr model, the quantum mechanical model does not define the exact path an
   electron takes around the nucleus. The electron does not orbit the nucleus in circles. It does
   predict the most probable locations of an electron when it is in a certain energy level. This
   region of a probable location for an electron is called an orbital.

7) Sec 11.7  The Hydrogen Orbitals (Atomic Orbitals)
   An atomic orbital is a region of space where there is a high probability of finding an electron.
   Atomic orbitals are characterized by a set of three integer quantum numbers (n, l, and m) that
   come from the mathematical solution to the Schrodinger equation.

   a) The principal quantum number, n  determines to a large extent the energy of the electron
      and is also related to how far from the nucleus we are likely to find the electron. (n = 1, 2,
      3, etc.)

   b) The secondary quantum number, l  describes the shape of the orbit (most probable
      locations of the electron). It also has some effect on the energy of the electron (sublevels). [l
      = 0(s), 1(p), 2(d), 3(f), etc. up to n-1 for each n value.]

   c) The magnetic quantum number, m  is related to the spacial orientation of the orbitals. It
      tells how many orbitals there are of a given type. (m = -l,..-1, 0, +1,..+l for each l value.)

   d) Summary
          n         l     Values of m                      Orbitals
          1         0     0                                1s

              2     0     0                                2s
                    1     -1, 0, +1                        2p 2p 2p

              3     0     0                                3s
                    1     -1, 0, +1                        3p 3p 3p
                    2     -2, -1, 0, +1, +2                3d 3d 3d 3d 3d

              4     0     0                                4s
                    1     -1, 0, +1                        4p 4p 4p
                    2     -2, -1, 0, +1, +2                4d 4d 4d 4d 4d
                    3     -3, -2, -1, 0, +1, +2, +3        4f 4f 4f 4f 4f 4f 4f

   The orbitals correspond to the appropriately named regions on the Periodic Table.

   Your book (pages 334-336) has pictures showing the relative sizes and shapes of orbitals for
   hydrogen. You also should have a handout that also shows these orbitals.
World of Chemistry Notes for Students                                            [Chapter 11, page 5]

8) Sec 11.8  More on the Model

   The model also allows for one more quantum number, most often called the "s" or spin
   quantum number. It takes into consideration that two electrons must have opposite spins in
   order to occupy the same orbital. The s quantum number can have values of -1/2 and +1/2.
   We will see how this works shortly.

9) Sec 11.9  Electron Arrangements in the First Eighteen Atoms on the Periodic Table
   The ways in which electrons are arranged around the nuclei of atoms are called electron
   configurations. Three rules/principles govern the filling of atomic orbitals.

   a) The Aufbau Principle  Electrons enter the orbitals of lowest energy first. (See diagram in
      book on page 345 for order of filling.)

   b) The Pauli Exclusion Principle  An atomic orbital may contain at most two electrons. To
      occupy the same orbital, two electrons must have opposite spins (clockwise or
      counterclockwise). 1s (89) [Arrows are sometimes used to indicate the spin of the electron.]

   c) Hund's Rule  When electrons occupy orbitals of equal energy, one electron enters each
      orbital until all the orbitals contain one electron with spins parallel.

   Examples  Give electron configurations of neutral atoms of the following:

       1   H=                         11   Na =                      26   Fe =


       2   He =                       15   P=                        50   Sn =


       8   O=                         19   K=                        83   Bi =

   Examples  Name the element whose atoms have these electron configurations:

   a) (18 Ar) 4s2 3d6            b) 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5

   A quick way to remember the order in which orbitals are filled with electrons is to draw the
   following chart. It is much easier to remember than the one on page 345.
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