## Wednesday, June 13, 2012

### Handy numbers to know

My thesis advisor has a mastery of an impressive library of handy physics tidbits, the kinds of things that have proven very useful to him and his group over the years.  These are facts that it's better to know from memory so you can hash problems out at a whiteboard without having to run to reference books.  Here are a few of his:
• One liquid liter of helium becomes about 700 gas liters at STP.
• One liquid liter of nitrogen becomes about 500 gas liters at STP.
• The latent heat of liquid helium is such that one Watt of heatung will boil off one liquid liter per hour.
• For thermal conduction through metals, when the temperature difference between $T_{\mathrm{hot}}$ and $T_{\mathrm{cold}}$ is not small, the rate of heat flow is given by $(T_{\mathrm{hot}}^{2} - T_{\mathrm{cold}}^{2})/(2 R_{\mathrm{th}}T)$, where $R_{th}$ is the thermal resistance.
• The Wiedemann-Franz rule for heat conduction through metals means that an electrical resistance of 150 n$\Omega$ corresponds to $R_{\mathrm{th}} T = 6$ K$^{2}$/W.
• 20 GHz is equivalent to 1 K in terms of energy.
• 1 meV is about 12 K in terms of energy.
Here are a few that I've adopted over the years in working with nanoscale physics:
• The conductance quantum, $G_{0} \equiv 2 e^{2}/h$, is about 12.9 k$\Omega$.
• A typical elastic mean free path for electrons in a polycrystalline good metal is 10-20 nm.
• Tunneling of electrons from a metal through vacuum drops off by about a factor of 7.2 for every additional Angstrom of distance.
• The density of states for gold at the Fermi energy is about $\nu = 10^{47}$/Jm$^{3}$.
• The Fermi velocity for gold is $v_{\mathrm{F}} = 1.4 \times 10^{6}$ m/s.
• You can go back and forth between the resistivity and the mean free path in a metal using the Einstein relation:  $(1/\rho) = e^{2} \nu D$, where $e$ is the electronic charge, $\nu$ is the density of states at the Fermi energy, and $D$ is the diffusion constant.  In 3d, $D = (1/3)v_{\mathrm{F}}\ell$.
• In goofy energy units, 8000 cm-1 is 1 eV.
• $\hbar c$ = 200 eV-nm.
There are others of varying degrees of obscurity.  Please feel free to add others in the comments.  To use math in the comments, you need to preface your LaTeX math with a \ and a (, and end your math expression with a \ and a ).

Anonymous said...

kT at 300K is about 26 meV

Anonymous said...

Peter Armitage said...

For optical spectroscopy (and other fields) one needs to go back and forth frequently between all different kinds of "goofy energy units". Frequently you only need rough ideas of relative magnitude. In this regard I remember

1 meV ~ 10 K ~ 10 cm^-1 ~ 200 GHz and corresponds to ~1mm wavelength of light in vacuum.

There are correct to numbers of order pi/e

David A. Muller said...

So the Fermi velocity in Au is $\pi/2 \alpha c$

the Planck energy ~ 2 GJ

Douglas Natelson said...

David, I think you're off by a factor of two; the Fermi velocity is more like 1.4e6 m/s for Au, right? On another note, I don't know why the script isn't running properly to render your LaTeX....

Douglas Natelson said...

Ahh. David, your LaTeX renders correctly in the "published" version of your comment (the one seen if I click on the title of the blog post), but not on the "preview" version (the one I can see right now as I edit this comment). Interesting.

Shon said...

LOL u guys r dinosaurs. Google no all this info on it already. its got the units on it 4 u so u dont have 2 no nothing about it no more. Google it knows all the units on it so u dont have 2 know nothing about it no more. u alwayz near a comp anytime now so u aint hav 2 no none of this no more.

Anonymous said...

This blog reminded my of this xkcd comic :)
http://xkcd.com/1047/

Peter Armitage said...

>LOL u guys r dinosaurs. Google no
>all this info on it already. its got
>the units on it 4 u so u dont have 2