PHYSICS 313
Problem set 6 2003
Given NOV. 17 2003
Due NOV. 26 2003

Problem 1:
Estimate the Fermi energy of the conduction electrons in sodium metal (there is 1 conduction electron per sodium ion). The atomic weight of sodium is 23 g mol$^{-1}$, the density is 0.950 g cm$^{-3}$.
Problem 2:
The isotope $^3He$ obeys Fermi statistics. At very low temperatures $^3He$ forms a liquid with a volume 4.62 $\times 10^{-29}$ m$^3$. The mass of a $^3He$ atom is 5.01 $\times 10^{-27}$ kg. Calculate the Fermi temperature and the Fermi velocity.
Problem 3:
A zipper contains a large number of links. The energy associated with opening a link is $\epsilon >0$. The zipper can only unzip from one end while the bulk of the interior remains closed. Find the mean and the variance of the number of open links at temperature $T$. (This is an oversimplified model of the opening of a double stranded DNA molecule when it replicates or synthesizes mRNA).