Modern Physics

Maxwell's Electromagnetic Wave Theory

What is the nature of light?  By the turn of the 20th century it seemed that one of the fundamental questions of physics had been answered.  James Clerk Maxwell (and Joseph Henry) had discovered electromagnetic induction.  That is, a changing magnetic field will induce an electric field.  A model of a light wave consisting of alternating electric and magnetic fields is shown below.
Key Concept:  Electromagnetic radiation is produced by a______________________ e______________ c____________.
 
Sketch a diagram of an electromagnetic wave:
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Click here to see a picture of this electromagnetic wave.
Maxwell's Electromagnetic wave theory was one of the crowning achievements of 19th century physics.  The theory described what light waves are made of.

Light as a Particle

In 1900 Max Planck was studying how light (E/M) energy was emitted from objects which absorb all incoming E/M energy.  He found Planck's work was largely disregarded until 1905 when a young physicist named A____________ E____________ used Planck's idea to some of the unusual aspects of the p________________ effect, whereby light falling on certain metals was found to cause e________________ to be ejected from the metal's surface.

The year 1905 was Einstein's annus mirabilis, for it saw the publication of five of his papers in the German yearbook of Physics, involving three developments of major importance.  In the same year he earned his Ph.D.  For his work in explaining the photoelectric effect Einstein was awarded the 1921 Nobel prize in physics.

In his application of Planck's quantum idea to the photoelectric effect, Einstein proposed

In the space below, write an expression for the energy of a quantum/photon in terms of frequency and in terms of wavelength.
E = E(f): E = E(l)

Where h = __________  ____ and is called P________ c___________ .

Examples:
 
1.  Calculate the energy of a photon of freq. 6.2E14 Hz. 2.  Convert this energy to electron-volts.
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Particle-Like Characteristics of Light

1.  The Photoelectric Effect

defn Photoelectric Effect:  Emission of e______________ from a metal surface when illuminated by light of sufficient e__________ .

This diagram shows the photoelectric effect on a metal surface.  Light is incident upon the surface and electrons are ejected.

2.  The Compton Effect

To investigate Photon momentum, single high energy photons (x rays or gamma rays) were used in collisions with electrons.  Instead of being totally absorbed, as in the photoelectric effect, the photons seemed to strike the e____________ and bounce off.  After the collision, the ejected electron carried part of the e__________, and the rest appeared as a new photon of lower f____________, (lower energy) than the incident photon.   This shows clearly that a high energy photon can act like a single p______________ .

key concept:  E__________ and m______________ were conserved in the collision.

In the space below sketch a diagram of a Compton collision.  Assume the photon has a frequency of 3.0E18 Hz, and that half the photon energy was absorbed by the electron.  The angle between the velocity vectors of the scattered photon and electron is 90o.
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Matter Waves

Moving particles have wave properties.  Louis DeBroglie made this proposal in 1924, based on his intuitive feeling that nature is symmetrical and that the dual nature of light is matched by the dual nature of matter.  Under ordinary circumstances the wave nature of moving objects not significant because their w_______________ are too s________.  It is only when moving particles are on a subatomic scale that their wave properties are observable and important.

To find the wavelength of matter we use the equation l = h/p.  This is called the matter wavelength or DeBroglie wavelength.

Example:  Find the matter wavelength of an electron moving at 3.0E6 m/s.
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This is a matter wave, not an E/M wave, but it will have wave properties that are similar to the corresponding portion of the E/M spectrum.  What type of E/M radiation corresponds to the wavelength calculated above?

In order for the wave properties of matter to be noticeable, the matter wavelength must be the same size or larger than the objects with which it interacts.  Diffraction is an important wave property to consider.  In order for a wave to diffract, its wavelength (l) must be larger than the slit through which it passes or larger than the object that it hits.  Sketch examples of these two types of wave diffraction below.
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Could the wave properties of a baseball cause it to diffract around a bat?  Why?
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For a simulation of the interference pattern caused by electron diffraction, click here.

Atomic Models

The English chemist J______ D__________ (1766-1844) was the first to advance a quantitative atomic theory.  His "B______________ B______ Model" represented atoms as uniform solid spheres of matter which combined in definite proportions to form compounds.  J.J. T______________ (1856-1940) is considered to have discovered the e______________ when, in 1897, he was able to provide proof of subatomic particles in cathode rays.  Thompson viewed the electron as a component of matter and was one of the first to suggest a theory as to the internal structure of the atom.  He believed the atom was a sphere of p______________ charge with negatively charged electrons embedded throughout, analogous to a positively charged d________ chock full of negatively charged r__________ (R__________ B______ Model).  This model was a good beginning, but calculations quickly showed that such an atom would require t________________ of electrons to be stable.  It is known that atoms have tens, even a hundred electrons, but atoms with thousands of electrons are not seen in nature.  The raisin bun model was soon replaced with a more useful one advanced by Thompson's student E__________ R________________.  It is with this model that we will begin our study of the atom in detail.

Radioactivity

defn Radioactivity:  Nucleus emits mass-energy in the form of a p______________ or p__________.

Three types of Radiation
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Name
Particle
Charge (e)
Mass (amu)
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Rutherford's Gold Foil Experiment

In the years 1906-1909, Ernest Rutherford and Hans Geiger (of geiger counter fame) showed that alpha particles are actually __________ nuclei.  A diagram of the apparatus used is shown to the right.  Rutherford began to study how alpha particles are scattered by thin sheets of metal.  He fired alpha particles at a sheet of g_________ foil only one fifty thousandth of an inch thick.  After passing through the foil alphas hit a zinc sulfide detection screen which converts the kinetic energy of the alphas to a brief flash of light called a s____________________ (Very much like Mr. Kichton's lectures!)   By counting the flashes of light at various angles Rutherford was able to record how the particles were being scattered.
The expectation was that the alphas should slam right on through the foil. In  Thomson's model, the electric charge in an atom is uniformly spread out over an area of size about 1E-10m.  With this charge density, one predicts deflections of 1 degree or less. In fact, although most of the alphas did go through as expected, some scattered through very large angles. Rutherford: "It was as incredible as if you fired a 15 inch shell at a piece of tissue paper, and it came back and hit you".  Click here for an animation showing alpha particles passing through a gold foil.

Results of Alpha scatter experiments:
Observation
Conclusion
1.  Most alpha particles are undeflected. 
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2.  Some alphas are deflected through large angles.  A few are even backscattered. (Deflected through angles greater than 90 degrees). 
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Rutherford's Planetary Model of the Atom

In the space below, sketch a diagram of Rutherford's planetary model (not to scale).
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Problems with the Rutherford Model

The Rutherford model does not account for the lack of emission of radiation as electrons move around the nucleus and the unique line spectrum of each element.

The Bohr Model (of hydrogen)

Working with Rutherford was a brilliant young theorist named Niels Bohr.  He introduced some of the new quantum physics into Rutherford's planetary model to fix the problems detailed above.  We are going to restrict our quantitative exploration of this model to hydrogen and mercury atoms.

The Bohr model of the hydrogen atom consists of a positively charged nucleus and a single electron revolving in a circular orbit.  Bohr made the following assumptions about the atom:

Bohr's Three Assumptions:

1. (a)  Only a limited number of specified o___________ are permitted. 1. (b)  Each orbit represents a particular energy state. 2.  An electron in a specified orbit does not lose e__________, even though it has an a_________________ toward the center.

3.  When an electron changes from one energy state to another, a photon with energy equal to the energies between the two states is e_________ or a______________.

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Energy Level Diagram for Hydrogen  (See PRT's)

Energy Levels

When gas atoms are bombarded by electrons or photons, the gas atoms can only accept energy only in fixed amounts.

defn Excitation:  The process of raising the e________ of electrons in atoms.
defn Ground State:  The ground state is the most stable state and is the lowest possible energy level.  Ground state is usually referred to as n = __.

defn Ionization potential:  The m____________ energy necessary to remove an electron from the atom.

Excitation energies are different for different gasses.  When an atom has an electron in an excited state it will subsequently release the energy as a p__________.

Click here for a simulation of a the orbits and energy structure in the hydrogen atom.

Line Series in Hydrogen

When electrons make energy transitions in hydrogen, the electromagnetic radiation emitted falls into one of three categories, or series.  Label the diagram with the names of the spectral series in hydrogen. 

Sketch a diagram of the Balmer series, using colored pencils.
 
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See Fig. 31-1 in Taffel
Calculate the energy of the first three lines in the series.  Using the energy level diagram for hydrogen, find the orbital transitions which correspond to these lines.  Remember, these are all Balmer series lines.
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More on Energy Levels in the Bohr Atom

In the Bohr model of hydrogen
Question:  What is the maximum number of different photons that an electron in the n=4 level can produce in a down transistion to the ground state? .
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Bohr's model of the atom, though a great improvement over the Rutherford model, still has some limitations.  I does not predict:

Atomic models which allow for these features have since been developed and were presented during your study of chemistry.

Cloud Model

In the electron cloud model, there is no specific orbit for an electron as it moves about the nucleus.  Instead there is a region of most probable electron location called a state.  Each electron occupies a state.  A state can hold no more than two electrons.  The high probability volume for an electron is called an electron cloud.  Electons in atoms behave like waves.  It is only when we remove an electron from the atom that is has particle-like characteristics.