Posted by: **zhak39** | March 14, 2011

## Loving Pi Day

By now, everyone knows that March 14 is Pi Day (3.14). Some people take it further and make it Pi second waiting until 1:59 to dive into the Pie Pi (3.14159). That’s problematic for me because actually it should be 1:59 a.m. and I am generally not surrounded by Pi Pie loving people at that time. I compromised and brought Pi Pies in for breakfast.

Any Excuse for a Party

For the really straightforward, this chocolate and whip cream confection…

Binary Pi Pie

As a nod to physics.

Peach Blueberry String Theory Pi Pie

For the right brained gourmet free radicals.

sPInach Pie

Nick, If you can explain what’s on the white board I will make you whatever kind of PI you like.

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here goes:

The stated question here looks to be “What percentage of electrons in a system at 300 degrees Kelvin have more than the Fermi energy of the system?”. Translated, the question they are asking is “what is different about this system at ~80 degrees Fahrenheit versus when it is at absolute zero, how many electrons have more energy than they otherwise would?”. I would imagine this would come up if you were trying to figure out how the electrical properties of a material change with temperature.

In detail:

You see, fermions (electrons, protons and neutrons, among other things) are only allowed to occupy particular “quantum states” in a system. The system we are familiar with where this happens is the “shells” of electrons surrounding the nucleus of an atom – these shells are quantum states.

On the left side of the board they are talking about Fermi energy, which is the energy of the highest occupied state in a system of fermions at absolute zero. In the case of an atom, the energy of the outermost electrons (at absolute zero).

To simplify things, however, they aren’t using the system of an atom because that would not fit on the board, they are using the easiest to work with system, a so called “one dimensional infinite square well”. Essentially, this is a system where the electrons are only allowed to bounce left and right and there is no possibility for them to escape – they are stuck in a well. You can thank Enrico Fermi for the formula they are solving for N, the “quantum number” of a particular state.

At the 5th line on the left they introduce an epsilon which means “a particular energy”. That line says, in effect, “the change in the quantum number per change in energy” equals the stuff on the right which you can thank Fermi and Dirac for. Then they switch over to the right side of the board and introduce the k_B (which you can thank Boltzmann for), in [k_B T] which is the energy of a particle with temperature T. They then find the ratio they are looking for using line 5 and *poof* must of it cancels out, everything about that particular energy (epsilon) goes away and they get this much smaller equation to answer their question in terms of just the temperature, Fermi energy and Boltzmann’s constant k_B.

By:

Nickon March 28, 2011at 2:30 am

Hmmm. Yes. Let me run this by my team of experts and get back to you.

And let me know what kind of PI you like.

By:

zhak39on March 28, 2011at 7:18 am

[…] He gave a stab at it. […]

By:

My Brilliant Genius Nephew « A Fine Kettle of Fishon April 2, 2011at 2:25 pm