19 Motivating Context for Unit III

A Venn-diagram showing the different sciences

This unit will focus on the electric field  \vec{E} and the electric potential  V . As described in the introduction, the electric force is the underpinning of chemistry, so I would like you to refresh some ideas about chemical bonds that you probably saw in your chemistry classes that we will use in this unit.

Another case that we will explore in some detail in this unit is gel electrophoresis: a process you have probably discussed in your biology class. This laboratory technique is fundamentally based upon the ideas of electric field and potential we will discuss in this unit. Thus, a review of the procedure based upon OpenStax Microbiology chapter 12.2 is included below for your review.

Molecular Bond Basics

describes a covalent bond as the overlap of half-filled atomic orbitals (each containing a single electron) that yield a pair of electrons shared between the two bonded atoms. We say that orbitals on two different atoms overlap when a portion of one orbital and a portion of a second orbital occupy the same region of space. According to valence bond theory, a covalent bond results when two conditions are met: (1) an orbital on one atom overlaps an orbital on a second atom and (2) the single electrons in each orbital combine to form an electron pair. The mutual attraction between this negatively charged electron pair and the two atoms’ positively charged nuclei serves to physically link the two atoms through a force we define as a covalent bond. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Orbitals that overlap extensively form bonds that are stronger than those that have less overlap. We calculated the shapes of these orbitals for simple molecules such as 1,3-butadine in-class during Unit I by modeling the electrons as a particle in a box!

The energy of the system depends on how much the orbitals overlap. Figure 1 illustrates how the sum of the energies of two hydrogen atoms (the colored curve) changes as they approach each other. When the atoms are far apart there is no overlap, and by the convention described in Unit I – Chapter 5 Some Energy-Related Ideas that Might be New or Are Particularly Important: The Potential Energy of Atoms and Molecules the potential energy of each atom is zero. As the atoms move together, the electron waves (orbitals) begin to overlap. Each electron begins to feel the attraction of the nucleus in the other atom. In addition, the electrons begin to repel each other, as do the nuclei. The result is the electron waves change shape in response.

While the atoms are still widely separated, the attraction is slightly stronger than the repulsion, and the energy of the system decreases. (A bond begins to form.) As the atoms move closer together, the overlap increases, so the attraction of the nuclei for the electrons continues to increase (as do the repulsions among electrons and between the nuclei). At some specific distance between the atoms, which varies depending on the atoms involved, the energy reaches its lowest (most stable) value. This optimum distance between the two bonded nuclei is the bond distance between the two atoms. The bond is stable because at this point, the attractive and repulsive forces combine to create the lowest possible energy configuration. If the distance between the nuclei were to decrease further, the repulsions between nuclei and the repulsions as electrons are confined in closer proximity to each other would become stronger than the attractive forces. The energy of the system would then rise (making the system destabilized), as shown at the far left of Figure 1.

A pair of diagrams are shown and labeled “a” and “b”. Diagram a shows three consecutive images. The first image depicts two separated blurry circles, each labeled with a positive sign and the term “H atom.” The phrase written under them reads, “Sufficiently far apart to have no interaction.” The second image shows the same two circles, but this time they are much closer together and are labeled, “Atoms begin to interact as they move closer together.” The third image shows the two circles overlapping, labeled, “H subscript 2,” and, “Optimum distance to achieve lowest overall energy of system.” Diagram b shows a graph on which the y-axis is labeled “Energy ( J ),” and the x-axis is labeled, “Internuclear distance ( p m ).” The midpoint of the y-axis is labeled as zero. The curve on the graph begins at zero p m and high on the y-axis. The graph slopes downward steeply to a point far below the zero joule line on the y-axis and the lowest point reads “0.74 p m” and “H bonded to H bond length.” It is also labeled “ negative 7.24 times 10 superscript negative 19 J.” The graph then rises again to zero J. The graph is accompanied by the same images from diagram a; the first image correlates to the point in the graph where it crosses the zero point on the y-axis, the third image where the graph is lowest.
Figure 1 (a) The interaction of two hydrogen atoms changes as a function of distance. (b) The energy of the system changes as the atoms interact. The lowest (most stable) energy occurs at a distance of 74 pm, which is the bond length observed for the H2 molecule.

Play with the energies of atoms and bonds

Below is a simulation where you can see the energies of atoms and their bonds. Play around with it. In this simulation, one atom is “pinned down” and the other is free to move.

  • Drag the free atom wherever you wish and let it go. It will move according to its potential energy.
  • You can see the overlap in the electron waves (electron clouds) at the bottom.
  • You can change the types of atoms using the menu in the upper right.
  • You can turn on the forces as well to see how the forces are responding to the potential energy.

You will notice that the atoms do not stay at a fixed distance; they bounce as skateboarders on a hill! You can even get neon atoms to “bond” although there is not a lot of room to do so! This is true; at small enough temperatures you can get neon to bond. At 24.56K it will actually become a solid. You can see O=O, on the other hand, has a much deeper well and is therefore a much stronger bond.


Problem 1: Comparing the energies of bound atoms vs. free atoms.

Basic Description of Gel Electrophoresis

We will explore this device in class, so it is probably beneficial if you have already familiar with how it works. This material is from OpenStax Microbiology – Chapter 12.2 Visualizing and Characterizing DNA, RNA, and Protein.

There are a number of situations in which a researcher might want to physically separate a collection of DNA fragments of different sizes. A researcher may also digest a DNA sample with a restriction enzyme to form fragments. The resulting size and fragment distribution pattern can often yield useful information about the sequence of DNA bases that can be used, much like a bar-code scan, to identify the individual or species to which the DNA belongs.

Gel electrophoresis is a technique commonly used to separate biological molecules based on size and biochemical characteristics, such as charge and polarity. Agarose gel electrophoresis is widely used to separate DNA (or RNA) of varying sizes that may be generated by restriction enzyme digestion or by other means, such as the PCR (Figure 2).

Due to its negatively charged backbone, DNA is strongly attracted to a positive electrode. In agarose gel electrophoresis, the gel is oriented horizontally in a buffer solution. Samples are loaded into sample wells on the side of the gel closest to the negative electrode, then drawn through the molecular sieve of the agarose matrix toward the positive electrode. The agarose matrix impedes the movement of larger molecules through the gel, whereas smaller molecules pass through more readily. Thus, the distance of migration is inversely correlated to the size of the DNA fragment, with smaller fragments traveling a longer distance through the gel. Sizes of DNA fragments within a sample can be estimated by comparison to fragments of known size in a DNA ladder also run on the same gel. To separate very large DNA fragments, such as chromosomes or viral genomes, agarose gel electrophoresis can be modified by periodically alternating the orientation of the electric field during pulsed-field gel electrophoresis (PFGE). In PFGE, smaller fragments can reorient themselves and migrate slightly faster than larger fragments and this technique can thus serve to separate very large fragments that would otherwise travel together during standard agarose gel electrophoresis. In any of these electrophoresis techniques, the locations of the DNA or RNA fragments in the gel can be detected by various methods. One common method is adding ethidium bromide, a stain that inserts into the nucleic acids at non-specific locations and can be visualized when exposed to ultraviolet light. Other stains that are safer than ethidium bromide, a potential carcinogen, are now available.

a) A diagram of the process of agarose gel electrophoresis. 1 – An agarose and buffer solution is heated and poured into a form. This result in a rectangular block with indents along one end labeled “S=sample wells”. 2 – When cooled, the agarose gel block contains small wells (S) where the sample will be place. 3 – Each sample is added to a separate well. Then the agarose gel is placed in a chamber that generates a charge across the gel. The samples are added using micropipettes. 4 – The solution within the chamber conducts the electric current generated by the chamber. The side nearest the sample well will have a negative charge; the other side will have a positive charge. 5 – DNA has a negative charge and will be drawn to the positive pole of the gel. Smaller DNA molecules will be able to travel faster through the matrix of the gel. 6 – One well will contain a DNA ladder, which has fragments of known size. This ladder is used to identify the sizes of the bands in the sample. The ladder looks like many bands in the gel; from top to bottom the sizes of the bands are – 2000 bp, 15000 bp, 1000 bp, 750 bp, 500 bp, 250 bp. The other lanes have a few bands of various sizes.
Figure 2 (a) The process of agarose gel electrophoresis. (b) A researcher loading samples into a gel. (c) This photograph shows a completed electrophoresis run on an agarose gel. The DNA ladder is located in lanes 1 and 9. Seven samples are located in lanes 2 through 8. The gel was stained with ethidium bromide and photographed under ultraviolet light. (credit a: modification of work by Magnus Manske; credit b: modification of work by U.S. Department of Agriculture; credit c: modification of work by James Jacob)



Problem 2: Reviewing gel electrophoresis.



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Physics 132: What is an Electron? What is Light? by Roger Hinrichs, Paul Peter Urone, Paul Flowers, Edward J. Neth, William R. Robinson, Klaus Theopold, Richard Langley, Julianne Zedalis, John Eggebrecht, and E.F. Redish is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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