• Electromagnetic radiation ­ energy that moves by means of electric and magnetic fields. "Light" is one small part of electromagnetic radiation. Other examples include X-rays, microwaves, and UV radiation

• Light ­ one form of electromagnetic radiation that is in the "visible" region of the radiation spectrum
  We can think of light as an oscillating wave. Thus, light waves can be characterized by their wavelength, frequency, and intensity.

• Wavelength (l) ­ distance between successive crests of a wave

• Frequency (n) ­ number of wave crests passing a point in space in 1 second
  One hertz is one cycle per second (1/s)

• The wavelength and frequency of light are related:
  wavelength x frequency = speed of light
  l x n = c (c = speed of light = 3.00 x 10⁸ m/s)

• Intensity (or amplitude) ­ the brightness of light. The more intense light is, the more energy it carries.

• Photons ; individual bundles of energy­ each photon has an energy that is directly proportional to the frequency: E(photon) = h x n(photon)
  where h is the proportionality constant between energy and frequency and is known as Planck's constant (h = 6.626 x 10^-34 J s)

Example Problems: Characteristics of Light

• Calculations involving nu and lambda
• Calculations of Electron Energy Level Changes

The frequency of red light is 4.57 x 10¹⁴ Hz. What is the wavelength of this color?

wavelength x frequency = c
wavelength = c/frequency
wavelength (l) = (3.00 x 10⁸ m/s)/(4.57 x 10¹⁴ s^-1) = 6.56 x 10^-7 m

E = h x frequency
E = hn
E = (6.626 x 10^-34 J s) x (4.57 x 10¹⁴ s^-1) = 3.03 x 10^-19 J

Binding energy = h x frequency
frequency = c/wavelength
wavelength (l) = hc/Binding energy

wavelength (l) = (6.626 x 10^-34 J s)(3.00 x 10⁸ m/s)/7.21 x 10^-19 J

l = 2.75 x 10^-7 m = 275 nm

The absorption spectrum of atomic hydrogen has a line at 121.6 nm. What is the frequency of the photons absorbed, and what is the energy difference, in joules, between the ground state and this excited state of atomic hydrogen?

1. Remember, we know the following relationships:
   E = hn
   n = c/l
   E = hc/l

2. First convert wavelength to frequency:
   n = (3.00 x 10⁸ m/s)/(121.6 x 10^-9 m) = 2.47 x 10¹⁵ Hz

3. Now find the energy of this frequency:
   E = (6.626 x 10^-34 J s) x (2.47 x 10¹⁵ Hz) = 1.63 x 10^-18 J

4. Now find the energy of the ground state of atomic hydrogen:
   E(ground) = ­ (2.18 x 10^-18 J/(n)²) where "n" is equal to one for the ground state

5. Now calculate the difference in energy between these two levels:
   Change in E = E - E(ground) = -1.63 x 10^-18 J - (-2.18 x 10^-18 J) = 5.5 x 10^-19 J

1. Each electron has the same mass and charge
   m = 9.109 x 10^-31 kg   e = 1.602 x 10^-19 C

2. Electrons behave like magnets. The magnetic properties of electrons arise from a property called spin. All electrons have spin of the same magnitude, but electron spin can have a positive or negative sign depending on which way the electron responds to a magnet.

3. Electrons have wave properties. Louis de Broglie (Nobel Prize 1929) first suggested that the wave-particle duality exhibited by photons should also be exhibited by electrons

4. Electrons bound to atoms have two additional characteristics:
   
   1. They are described by delocalized waves. Most of the volume of an atom is filled with wave-particle electrons­"a three dimensional wave". Orbitals are the three-dimensional shape an electron "fills" in an atom. Each atomic energy level can be associated with a specific three-dimensional atomic orbital

   2. Their energies are quantized. Quantization of energy is a property of bound electrons. A bound electron is one held in a specific region of space by coulombic attraction for a nucleus in an atom or molecule.

Because of their wave properties, electrons are always spread out rather than localized in one particular place. The Uncertainty principle states that the more accurately we know position, the more uncertain we are about velocity and vice versa. In a universe subject to uncertainty, many things cannot be measured exactly, and it is never possible to predict with certainty exactly what will occur next.

• The quantum number for energy is called the principal quantum number (n)
  
• E_n = -2.18 x 10^-18 J/n²
  
• The most stable energy for an atomic electron corresponds to n = 1 and each successively higher value of n describes a less stable energy state.
  
• The principal quantum number must be a positive integer: n = 1, 2, 3, ...
  
• As n increases, the energy of the electron increases, its orbital gets bigger, and it becomes less stable.

• The quantum number that indexes the shapes of atomic orbitals is called the azimuthal quantum number (l)
  
• The azimuthal quantum number (l) can be any positive integer smaller than n: l = 0, 1, 2, ..., (n-1)
  
• Historically, orbital shapes have been identified with letters rather than numbers
  

• A description of all electrons in an atom is called an electron configuration
  
• There is an infinite number of acceptable sets of quantum numbers but only one set, the ground-state configuration, describes an atom in its most stable form
  
• The Pauli Exclusion Principle states that each electron in an atom must have a unique set of quantum numbers. Also stated as no two electrons in an atom may have identical sets of all four quantum numbers.
  
• The Aufbau principle states that each successive electron is placed in the most stable orbital whose quantum numbers have not already been assigned to another electron
  
• Degenerate orbitals are orbitals with identical energy
  

1. List the values of all quantum numbers for every one of the atom's electrons
   
2. Shorthand notation using orbital symbols followed by superscripts designating how many electrons are in each orbital
    ₁H  1s¹
    ₆C  1s² 2s² 2p²
   ₂₈Ni  1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁸
   
3. The filled shell configuration uses Noble gases as markers of complete electron orbitals
    ₁H  1s¹
    ₆C  [He] 2s² 2p²
   ₂₈Ni  [Ar] 4s² 3d⁸
   
4. Place the electrons in an energy level diagram. Each electron is represented by an arrow. The direction of the arrow indicates the value of the spin orientation quantum number. For m_s = +1/2, the arrow points upwards and for m_s = -1/2, the arrow points downwards. Paired electrons are electrons in the same energy level with opposing spin, opposing spins cancel, so paired electrons have zero net spin

   

• Hund's Rule: For an atom in its ground-state configuration, all unpaired electrons have the same spin orientation
  
• The energy spacing between sets of orbitals gets smaller as the principal quantum number increases. At the same time, orbital splitting between different l values increases as nuclear charge increases

• We can write electron configurations of atomic ions using the same procedures as for neutral atoms, as long as we take into account the number of electrons added or removed.
  
• Atoms and ions that have the same number of electrons are said to be isoelectronic
  
• In neutral transition metal atoms, the (n-1)d and (n)s orbitals are degenerate with (n)s slightly more stable.
  
• For transition metal cations, however, the (n-1)d orbitals are always more stable than the (n)s orbital

• The physical properties and the chemical properties of the elements show regular periodic variations. All of these regularities can be attributed to variations in electron configurations and nuclear charges.
  
• Two fundamental features of orbitals form the basis of periodicity:
  
  1. As Z increases, atomic orbitals become smaller and more stable
     
  2. As n increases, atomic orbitals become larger and less stable

• Moving from left to right across a row, orbitals become smaller and more stable
  
• Moving from top to bottom down a column, orbitals become larger and less stable
  
• Atomic radii decrease moving from left to right across a row of the periodic table
  
• Atomic radii increase moving from top to bottom down a column of the periodic table
  
• The minimum amount of energy needed to remove an electron from a neutral atom is called the first ionization energy
  
• First ionization energy increases from left to right across a row of the periodic table
  
• First ionization energy decreases from top to bottom down a column of the periodic table
  
• A multielectron atom can lose more than one electron but ionization becomes more difficult as cationic charge increases. As the number of electrons decreases, each electron feels a greater coulombic attraction to the nucleus, resulting in a larger ionization energy.
  
• The energy required to remove an electron from a negative ion is called the electron affinity
  
• Electron affinity tends to increase from left to right across a row of the periodic table
  
• Properties change regularly with Z across an isoelectronic series, reflecting changes in Z without corresponding changes in the number of electrons