Polarizability of a carbon atom
Try rubbing a plastic pen through your hair, and you'll discover that you can pick up a tiny scrap of paper when the pen is about one centimetre above the paper. From this simple experiment you can estimate how much an atom in the paper is polarized by the pen! You will need to make several assumptions and approximations.
a) Assume that the center of the outer electron cloud (q = -4e) of a carbon atom shifts a distance s when the atom is polarized by the pen. Compute s algebraically in terms of the charge Q on the pen. (Use the following as necessary: m, g for acceleration due to gravity, h for the distance from the carbon to the pen, e for the charge of the electron, Q, 0, and ?. )
s =
b) Suppose that the pen carries 10 8 C of charge (Q). Evaluate s numerically. How does this compare with the size of an atom or a nucleus?
s =
c) Compute the polarizability of a carbon atom. Compare your answer to the gauged value of 1.96 ? 10 -40C·m/(N/C) (T. M. Miller and B. Bederson, "Atomic and molecular polarizabilities: a review of recent advances," Advances in Atomic and Molecular Physics, 13, 1?55, 1977).
? =
d) Carefully list all approximations and assumptions you made.