Download P202 Lecture 2

Lecture 21– Examples Chpt. 7
Lecture 21– Examples Chpt. 7
Langmuir Adsorption
q
P=[kBT/l3] [q/(1-q)] exp(-eo/kBT)
http://en.wikipedia.org/wiki/Langmuir_adsorption_model
Cryopumps
Why do they pump N2 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 q for a given
number of atoms adsorbed)
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?
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?
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?
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/4p, 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.)
YF(x1,x2) = - YF(x2,x1)
BOSONS (even-integert multiple of hbar/2=s=0, hbar, 2*hbar, 3*hbar etc.
YB(x1,x2) = YB(x2,x1)
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.
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/4p, 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.)
YF(x1,x2) = - YF(x2,x1)
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.
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