GR9277 #23



Alternate Solutions 
claire 20090912 11:31:59  If you don't want to have to bother with the big numbers for the approximation, you can use your knowledge that for room temperature (~300K) you have kT=eV (this is a useful thing to know). And you know that an electron mass is .5MeV/c.
The problem uses 80,000K, but do it for 90,000, since thats easier with the numbers you know.
Then kT~, so = ~ ~ 2 10 m/s, option (E).  

Comments 
rwmurphy 20121108 12:58:40  I have a slight issue with the wording of this problem: it only states that the Fermi temperature of copper is at 80000K, not that the copper is actually at the fermi temperature. I mistakenly thought the ETS was just trying to be tricky and asking for a reasonable drift velocity in Cu, which then (A) would be the answer.
*sigh*
When I look at it now, it easy to assume that they mean copper is at that temperature, but under a crunch for time, your brain does funny things! Either way, they should make it less ambiguous.
NSF Fellow 20130918 11:13:11 
It says conducting electrons! they are at fermi energy!

NoPhysicist3 20170323 09:38:59 
same sh*t man

NoPhysicist3 20170323 09:42:00 
but as i noticed GRE problems tend to use all information given in the task

  Quark 20111025 14:35:18  Why do we use kT for the energy and not for the three translational degrees of freedom in finding the kinetic energy?
liliapunto 20130714 03:15:52 
This is exactly what I did and what I want to ask about.

Prufrock 20130903 15:04:01 
Because condensed matter physicists don't recognize factors as small as 3/2  and in this problem it is certainly true that the 3/2 is insignificant.

NSF Fellow 20130918 11:14:37 
it's not a gas!

NSF Fellow 20130918 13:08:25 
and it says the Fermi temperature of Cu, not the temperature Cu is at.

  neon37 20101111 03:59:18  Here we can clearly get away with order of magnitude approximation, so dont bother about any numbers except ones. You will get the answer in less than a minute.   nyuko 20091030 10:10:08  I did this problem in seconds. I just remember the typical Fermi speed for electron in metals is of the order
I think there are some typical values for physicists to remember. Fermi speed of electrons in metal is one.   claire 20090912 11:31:59  If you don't want to have to bother with the big numbers for the approximation, you can use your knowledge that for room temperature (~300K) you have kT=eV (this is a useful thing to know). And you know that an electron mass is .5MeV/c.
The problem uses 80,000K, but do it for 90,000, since thats easier with the numbers you know.
Then kT~, so = ~ ~ 2 10 m/s, option (E).   ramparts 20090802 17:36:13  I did this much more quickly by just looking at orders of magnitudes. Ignoring dimensionless constants (which will never change the answer by a factor of 2), temperature depends on the energy divided by the Boltzmann constant, and the energy is roughly kinetic energy, mv^2. So we have
Plug in the appropriate factors of 10, and you get . Excellent.
I have no idea if the physics is right, but the dimensions work out and the answer is right ;)
Albert 20091103 05:05:17 
Yes, your method is really bad. Not only your physics is abominable, your math is plain wrong too. You got the formula wrong and that's besides the fact that you did basically the same thing as Yosun, just didn't write the steps. And then got it all mixed up. I wonder how you ever reached the answer (or did you?). Sorry, but it's important that truth be spoken.

Ryry013 20191017 10:04:21 
This gives an answer around 10^29 I believe, definitely wrong (；・﹏・)

  none 20081019 23:01:52  If you write things a bit differently you get . The only answer with the right order of magnitude is (E)   student2008 20081014 09:58:44  Actually, ETS means the average velocity modulus, , which can be obtained using the Maxwell distribution. Though such rigorous formula isn't relevant for the real exam, of course.
student2008 20081014 10:08:31 
Even more precise would be and , but apparantely it's not for the exam :)

student2008 20081015 00:14:53 
Stupid me, all I wrote above is wrong. In fact, the concept of Fermigas (and Fermienergy) of electrons requires , not . What is relevant here is the lowtemperature Fermi distribution of electrons (which is true up to melting temperatures: ), not the Maxwell distribution. However, the problem asks about the mean speed of the electrons. And these are the electrons near the Fermi surface, since only their energy may change (under the notextremelyhigh voltage). So, Yosun's solution is right, with this reservation.

  prismofmoonlight 20071031 11:22:40  I think T_F is 8E4, not 8E5 as given in your equation (though the change is not enough to affect the approximation too terribly much).
Thanks for the great site!  

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