4.2.4.P8
A. When a DNA molecule is in water, each base pair grabs a pair of electrons from surrounding water molecules, releasing a pair of hydrogen ions. As a result, the DNA molecule has a net charge. On the web, find a reliable site (and say why you think it is reliable) that tells you the number of base pairs in a typical human chromosome. (Not the Y chromosome!) To get a sense of the charge involved, imagine that you had two coiled up chromosomes, each with a charge of 2 extra electrons per base pair. Suppose you held them fixed in a vacuum one micrometer apart. For simplicity, model the chromosomes as point charges. Estimate the electric force between the two chromosomes in this example. Explain why this kind of electrostatic repulsion is not a problem when DNA is in its natural environment.
B. We know that within the limits of measurement, the magnitudes of the negative charge on the electron and the positive charge on the proton are equal. Suppose, however, that the magnitude of the charge on the proton was bigger than that on the electron. On the web, find a reliable site (and say why you think it is reliable) that tells you the number of electrons and protons in a copper atom and the mass of a copper atom. From this data, estimate the total number of protons and electrons in a penny, and estimate the net charge there would be on a penny if the charge on the proton was bigger than the charge on an electron by 1 part in a million. With what force would two copper pennies then repel each other if they were held one meter apart? Since the size of a penny is small compared to one meter, we can treat the pennies as point charges.
Since pennies do NOT repel each other with any detectable force, what can you conclude about the charges on a proton and on an electron?
C. You should have found that the force between the DNA molecules was very small and the force between the pennies was very large. This might seem surprising at first, since the number of base pairs (and therefore the number of electrons) was so large, while the discrepancy between the charges assumed in part B were so small. From the calculations you have carried out, figure out WHY the result in part A is so much smaller than the result in part B and explain why the result actually makes sense.
You may take the Coulomb constant to be kC ~ 9 x 109 N-m2/C2.
Joe Redish 8/7/11
Wolfgang Losert 10/14/12
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