Electronic Structure

The content that follows is the substance of General Chemistry Lecture 24. In this lecture we Introduce the concepts of electromagnetic radiation, wavelength, frequency and the Photoelectric Effect.

Electromagnetic Radiation

Electromagnetic waves are produced by the motion of electrically charged particles. These waves are also called "electromagnetic radiation" because they radiate from the electrically charged particles. They travel through empty space as well as through air and other substances.

Electromagnetic Radiation

Scientists have observed that electromagnetic radiation has a dual "personality." Besides acting like waves, it acts like a stream of particles (called "photons") that have no mass. The photons with the highest energy correspond to the shortest wavelengths.
There are some general properties shared by all forms of electromagnetic radiation:

      1. It can travel through empty space. Other types of waves need some sort of medium to move through: water waves need liquid water and sound waves need some gas, liquid, or solid material to be heard.

      2. The speed of light is constant in space. All forms of light have the same speed of 299,800 kilometers/second in space (often abbreviated as c). From highest energy to lowest energy the forms of light are Gamma rays, X-rays, Ultraviolet, Visible, Infrared, Radio. (Microwaves are high-energy radio waves.)

      3. A wavelength of light is defined similarly to that of water waves---distance between crests or between troughs. Visible light (what your eye detects) has wavelengths 4000-8000 Ångstroms. 1 Ångstrom = 10-10 meter. Visible light is sometimes also measured in nanometers(nm): 1 nanometer = 10-9 meter = 10 Ångstroms, so in nanometers, the visible band is from 400 to 800 nanometers. Radio wavelengths are often measured in centimeters: 1 centimeter = 10-2 meter = 0.01 meter. The abbreviation used for wavelength is the greek letter lambda: λ.

 

Besides using wavelength to describe the form of light, you can also use the frequency--the number of crests of the wave that pass by a point every second. Frequency is measured in units of hertz (Hz): 1 hertz = 1 wave crest/second. For light there is a simple relation between the speed of light (c), wavelength (λ), and frequency (v):

v = c/λ.

Since the wavelength λ is in the bottom of the fraction, the frequency is inversely proportional to the wavelength. This means that light with a smaller wavelength has a higher (larger) frequency. Light with a longer wavelength has a lower (smaller) frequency.

spectrum

The Visible Spectrum
Visible light waves are the only electromagnetic waves we can see. We see these waves as the colors of the rainbow. Each color has a different wavelength. Red has the longest wavelength and violet has the shortest wavelength. When all the waves are seen together, they make white light.
When white light shines through a prism, the white light is broken apart into the colors of the visible light spectrum. Water vapor in the atmosphere can also break apart wavelengths creating a rainbow.

Prism

colors and their wavelengths

color

l(Å)

v(*1014 Hz)

Energy (*10-19 J)

violet

4000 to4600

7.5 to6.5

5.0 to4.3

indigo

4600 to4750

6.5 to6.3

4.3 to4.2

blue

4750 to4900

6.3 to6.1

4.2 to4.1

green

4900 to5650

6.1 to5.3

4.1 to3.5

yellow

5650 to5750

5.3 to5.2

3.5 to3.45

orange

5750 to6000

5.2 to5.0

3.45 to3.3

red

6000 to8000

5.0 to3.7

3.3 to2.5

 

Planck’s Equation
In Planck's assumption, radiant energy is emitted in small bursts, known as "quanta". Each of the bursts called a "quantum" has energy E that depends on the frequency f of the electromagnetic radiation by the equation: 

E = hv


where h is a fundamental constant of nature, the "Planck constant".  6.626e-34 J.s
This equation is later found to be true for all EM radiant energy emitted or absorbed.


Max Planck
Photo of Max Planck.
Courtesy of AIP Emilio Segre Visual Archives, W.F. Meggers Collection.

 

 

 

 

Planck's equation implies the higher the frequency of a radiation, the more energetic are its quanta.

The Photoelectric Effect


    1. It's been determined experimentally that when light shines on a metal surface, the surface emits electrons.  This is the photoelectric effect.
      Characteristics of Photoelectric effect
      1. The electrons were emitted immediately

      2. Increasing the intensity of the light increased the number of photoelectrons, but not their maximum kinetic energy.

      3. When Na is the metal red light will not cause the ejection of electrons, no matter what the intensity.

      4. Weak violet light will eject only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths.
    2. duality of light

      Waves vs Particles – If light only has wave properties then only the intensity of the light and not its frequency should create the photoelectric effect.  So light must also have particle characteristics.



      difference between energy and intensity

       

      The term intensity has a particular meaning here: it is the number of waves or photons of light reaching your detector; a brighter object is more intense but not necessarily more energetic. Remember that a photon's energy depends on the wavelength (or frequency) only, not the intensity. The photons in a dim beam of X-ray light are much more energetic than the photons in an intense beam of infrared light.

Based on Planck's work, Einstein proposed that light also delivers its energy in chunks; light would then consist of little particles, or quanta, called photons, each with an energy of Planck's constant times its frequency. Light falling on the electrode, and consisting of photons having the correct amount of energy, knocks the electrons out. The electrons of metal just absorb the photons and take all their energy. So when light intensity increases, the number of photons having proper energy increases too. They knock out a greater number of electrons giving each of them the same energy by the smaller intensity of light. Whereas when light frequency increases, the energy of photons increases too. Yet the photons absorbed by the electrons give them more energy than before. (They give them higher speed.)

Using the Light Equations

Image result for light frequency and wavelength equations

Here are some practice problems:

Problems:

    1. Excited sodium atoms may emit radiation having a wavelength of 589 nm.
      a) What is the wavelength in meters?   b) What is the frequency of this light?
      c) What region of the spectrum is this in?   d) What is the energy of this light?

    2. A radio station has a frequency of 96.5 MHz. Find the wavelength and E.

    3. Microwaves have a frequency of around 2.5 GHz. What is the wavelength? (1 GHz = 109 Hz)

    4. What is the energy associated with 688 nm light? What color light is this?

    5. A certain photon of radiation has energy of 4.65 x 10-15 J. What is the wavelength of this light, in nm?

    6. A certain light has an energy of 4.56 x 10-19 J. What color is this light? (Hint: find wavelength in nm.)

     


 

Key