1. Lecture 21– Examples Chpt. 7

3. Langmuir Adsorption http://en.wikipedia.org/wiki/Langmuir_adsorption_model P=[k B T/ 3 ] [  /(1-  )] exp(-  o /k B T) 

4. Cryopumps Why do they pump N 2 more effectively than He? He is smaller/lighter etc. (5 answers) Boiling/freezing points are different (and He is much lower) (3 answers) Other (2 answers). Why do they use activated carbon (i.e. highly porous graphite)? it’s porous (3 answers) It has a very large surface area (2 answers; therefore small  for a given number of atoms adsorbed)

5. Osmosis Consider a vessel filled with a solvent and separated into two sides by a membrane through which the solvent can pass. Now, what happens if you add to one side other atoms that are unable to pass through that membrane?

6. Osmosis Consider a vessel filled with a solvent and separated into two sides by a membrane through which the solvent can pass. Now, what happens if you add to one side other atoms that are unable to pass through that membrane?

7. Spin-statistics theorem As we discussed in P301, all sub-atomic particles with which we have experience have an internal degree of freedom known as intrinsic spin, which comes in integral multiples of hbar/2 (i.e. h/4 , so it has dimensions of angular momentum). The value of this spin has remarkably powerful consequences for the behavior of many-body systems: FERMIONS (odd-integer multiple of hbar/2=s=hbar/2; 3hbar/2; 5hbar/2 etc.)  F (x 1,x 2 ) = -  F (x 2,x 1 ) BOSONS (even-integert multiple of hbar/2=s=0, hbar, 2*hbar, 3*hbar etc.  B (x 1,x 2 ) =  B (x 2,x 1 ) This connection between the intrinsic spin of the particle and the “exchange symmetry” of the many-body wavefunction is known as the spin-statistics theorem. We won’t try to prove it (it comes out of relativistic quantum field theory), but over the next couple of weeks we will look at some of its important consequences.

8. Spin-statistics theorem As we discussed in P301, all sub-atomic particles with which we have experience have an internal degree of freedom known as intrinsic spin, which comes in integral multiples of hbar/2 (i.e. h/4 , so it has dimensions of angular momentum). The value of this spin has remarkably powerful consequences for the behavior of many-body systems: FERMIONS (odd-integer multiple of hbar/2=s=hbar/2; 3hbar/2; 5hbar/2 etc.)  F (x 1,x 2 ) = -  F (x 2,x 1 ) Pauli Exclusion Principle: NOTE That an important consequence of the above symmetry exchange requirement on fermion many-body wave functions is that you cannot have two fermions or more in the same one-body state. Thus fermion occupation numbers are limited to the values 0 or 1.

10. Spin-statistics theorem Feynman Lectures on Physics:...An explanation has been worked out by Pauli from complicated arguments of QFT and relativity...but we haven’t found a way of reproducing his arguments on an elementary level...this probably means that we do not have a complete understanding of the fundamental The essential argument is that the QFT is assumed to be Lorentz invariant, and transition amplitudes need to remain properly ordered in time in all Lorentz frames: http://hep.uchicago.edu/cdf/frisch/p363/jian_testbmr.pdf