

All Solutions of Type: Advanced Topics  2  Click here to jump to the problem!  GR8677 #23

Advanced Topics}Solid State
Actually, one can figure this one out with only knowledge of lower div baby physics.
(A) Electrical conductivities for conductors, semiconductors, and insulators go (in general), like this . Thus, copper should be more conductive than silicon. This is true (but one is trying to find a false statement).
(B) The resistivity , thus the conductivity, . As increases, decreases. This is true.
(C) Silicon is a semiconductor, and thus it probably does not follow the same relations as (B). In fact, semiconductors have negative temperature coefficient of resistivities. Thus, , which implies that for temperature increase.
(D) Doping a conductor like copper will just make it cheap. Think of cheap wire.
(E) Doping a semiconductor, however, can make it more conductive.

3  Click here to jump to the problem!  GR8677 #38

Advanced Topics}Logical Circuit
(A) This is the OR gate. Triangle with fatend on input side denotes OR.
(B) Triangle with fatend closer to output side denotes AND. (Pointy tip points to each input.)
(C) A 2 bitadder involves more operations than this...
(D) A flipflop is a sort of sandal that flips and flops. It might also flip the floating point.
(E) A fanout describes the maximum number of outputs a circuit can excrete. (Fanin would be inputs.)

6  Click here to jump to the problem!  GR8677 #85

Advanced Topics}Nuclear Physics
Pair production only occurs above a certain energy on the order of MeV. Thus, all except choices (B) and (C) remain.
The photoelectric effect is dominant for low energies, so its crosssection must be line (1). Choose choice (B).

7  Click here to jump to the problem!  GR8677 #10

Advanced Topics}Particle Physics
Recall that in gammaray production, the excited nucleus jumps to a lower level and emits a photon . In internal conversion, however, an orbital electron is absorbed and ejected along with an Xray.

10  Click here to jump to the problem!  GR8677 #34

Advanced Topics}Particle Physics
Regularly, electrons are emitted in any direction. Thus, there is infinite symmetry. In the case of a magnetic field, electrons are more likely to be emitted in a direction opposite to the spin direction of the decaying atom. Place the atom in an xy plane, with its spindirection pointing along the zaxis. If the electron is mostly emitted in the z axis, then reflection symmetry is violated since it's not (mostly) emitted in the +z axis, i.e., not mirrored across the xy plane. Choice (D).
(This is due to Joe Bradley.)

12  Click here to jump to the problem!  GR8677 #63
 Advanced Topics}Particle Physics
If one knows little about particle physics, one can make (at least) the following deductions, wherein one recalls the composites of each particle:
(A) A muon is a lepton. Leptons, along with quarks, are considered the fundamental particles.
(B) PiMeson consists of a quark and its antiparticle. (Contribution to this part of the solution is due to user danty.) Moreover, a pimeson is a hadron. Hadrons interact with the strongforce, and all of them are composed of combinations of quarks. (The fundamental particles are classified as quarks and leptons.)
(C) A neutron is made up of 3 quarks.
(D) A deuteron consists of a proton and a neutron. (tritium is two neutrons and a proton, while regular Hydrogen is just an electron and proton)
(E) An alpha particle consists of electrons and protons and neutrons.
Choice (A) remains. Choose that.
If one has some time, one might want to remember the elementary particles involved in the Standard Model. There are six quarks and six leptons. Three of the leptons are neutrinos and the other three are the electron, the tau, and the muon. (Also, in a decay similar to betadecay, a muon is emitted instead of an electron. Charge conservation works since a muon is like an electron except it is about 200 times more massive.)
Wikipedia has a good reference on this:
\begin{verbatim}
http://en.wikipedia.org/wiki/Fundamental_particle
\end{verbatim}

15  Click here to jump to the problem!  GR8677 #78

Advanced Topics}Solid State Physics
A ntype semiconductor is a material with negativecharge carriers, such as electrons. A ptype semiconductor is a material with positivecharge carriers, such as holes (positrons).
In band theory, ntype semiconductor impurities are (electron) donors, while ptype semiconductor impurities are (electron) acceptors.
The setup is as follows:
Impurities add in more levels to the energy bands. Without impurities, one has just a valance band and a conduction band with an energy gap in between. The impurities supply an extra energy level in between the conduction and valance bands. In an ntype semiconductor, the material becomes conducting when there are electrons in the conduction band; the impurity helps the material become conducting by supplying it with electrons.
Essentially, one starts with a lattice of pure semiconductor atoms, say Silicon. Silicon has four valance electrons and forms a decent crystal lattice. Pluck out a few silicon atoms and replace them with some impurities, like Arsenic, which five valance electrons. The extra electron from each impurity atom is free to roam around. In fact, these extra electrons act as donors to the conduction band. This is choice (E).

17  Click here to jump to the problem!  GR8677 #19

Advanced Topics}Astrophysics
It takes 4 H's to create a Helium nucleus in the sun's primary thermonuclear reactions. One either remembers this or can derive it from conservation of mass. The atomic mass of Hydrogen is 1 (since it has just 1 proton), while the atomic mass of Helium is 2 (2 protons, 2 neutrons).

18  Click here to jump to the problem!  GR8677 #52

Advanced Topics}Solid State Physics
Recall the definition of a primitive cell to be the unit cell divided by the number of lattice points in a Bravais lattice. A Bravais lattice is just a lattice that looks isotropic from any pointeverywhere the same no matter the pointperspective.
Simple cubic has 1 lattice point to generate its Bravais lattice.
Bodycentered cubic has 2 lattice points to generate its Bravais lattice. (One can keep on tesselating the a lattice point on one corner and the lattice point on the body center to generate the whole BCC lattice.)
Facecentered cubic has 4 lattice points to generate its Bravais lattice. (One can keep on tesselating the lattice point on each face surrounding a corner lattice point.)
So, anyway, from the above, one finds choice (C) for BCC's unit cell.

24  Click here to jump to the problem!  GR8677 #78

Advanced Topics}Particle Physics
A few lines from the Particle Physics chapter of my upcoming book (title tentative, to be publicized on this website eventually), Reviewing Forgotten Physics for the GRE, Prelim's and Qualifier's:
Baryons and mesons are hadrons. (Hadrons are particles that interact with the strong nuclear force.) Baryons have a baryon number of , while mesons have . Nucleons (which are baryons) have , while antinucleons (antineutrons and antiprotons) have .
Leptons (electrons, neutrinos, muons, and tau's) interact with the weak nuclear force. There are three kinds of lepton numbers. There is the electron lepton number and there is a muon lepton number, as well as a neutrino lepton number.
Electrons and the electron neutrino have , while positrons (antielectrons) and the electron antineutrino have . All other particles have
Conservation of baryon number or lepton number is just summing up either the baryon number or the lepton number on both sides of the reaction.
Conservation of the numbers above explain for why a reaction like must occur in lieu of or or or .
For the first reaction, the electron Lepton numbers are , and thus is conserved. (Muon Lepton numbers are )
For the second reaction, the muon lepton numbers are , but that does not add up, and so is not conserved.
For the third reaction, the electron Lepton numbers are , but that does not add up, and so is not conserved.
As an exercise, one can calculate the fourth and fifth reaction.
(If you're beginning to feel like this is more alchemy than physics, then note that the Standard Model of particle physics is just a transitory theory, like alchemy was to chemistry. It is to be replaced soon with a less adhoc theory, perhaps by you.)
With respect to this question on the GRE exam, one sees that lepton number would not be conserved for any of the possible cases of the latter reactions.

25  Click here to jump to the problem!  GR8677 #25

Advanced Topics}Particle Physics
Choice (A) and (C) involve atoms, which are quite massive. Choice (B) involves protons, which are also pretty massive. Massiveness eliminates three choices, leaving just (D) and (E).
Neutrinos are massless, but muons aren't. Both positrons and electrons have the same mass. Massiveness has lost its charm. (No pun intended.)
According to David Schaich, the SuperKamiokande
and the Antarctic Muon and Neutrino Detector Array (AMANDA) are both located deep down underground to avoid interaction with other particles. Thus, with the hindsight of this bit of trivia, choice (D) is correct.

26  Click here to jump to the problem!  GR8677 #39

Advanced Topics}Fourier Series
There's no need to go through the formalism of integrating out the coefficients.
One can tell by inspection that the function is odd. Thus, one would use the Fourier sine series. This leaves choices (B) and (A).
Choice (A) is trivially zero since for all integer n, . Choice (B) remains.

29  Click here to jump to the problem!  GR8677 #91
 Advanced Topics}Strangeness
Elimination time:
(A) Only muons, neutrinos and electrons are leptons. Moreover, the pimeson is a meson, which is a hadron with baryon number 0. (Hadrons interact with the strong nuclear force, while leptons interact with the weak nuclear force, em force, and possibly even the gravitation force.)
(B) The lambda has spin 1/2, as do most baryons. (The mesons have spin 0, but positive strangeness numbers.)
(C) Lepton number is already conserved, since none of the particles involved have nonzero lepton numbers. Thus, introducing a neutrino would violate (electron) lepton number conservation.
(D) No reason why...
(E) Only hadrons have nonzero strangeness (strangeness was proposed when strong particles interact as if weak particlesi.e., instead of having superfast decay times characteristic of strongforce particles, their decay times appeared as if weakforce decays). Protons have 0 strangeness, as do pimesons, even though they are both hadrons. However, the lambda has 1 strangeness. Thus, strangeness is not conserved. 
31  Click here to jump to the problem!  GR8677 #97
 Advanced Topics}Solid State Physics
This is a result one remembers by heart from a decent solid state physics course. It has to do with band gaps, which is basically the core of such a course.
Then again, one can easily derive it from scratch upon recalling some basic principles: , , where k is the wave vector, E is the energy, m is the mass, and p is the momentum.
From the above, one has .
Set the two 's equal to get . Cancel out the 's to get , after differentiating with respect to k on both sides.
Alternatively, one can try it Kittel's way:
Start with . Then, . Thus, the effective mass is defined by .





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