44
Preparing for the Physics GRE: Day 4 Advanced Topics: Atomic, Particle, and Nuclear Physics Daniel T. Citron [email protected] 3/25/15 http://greprep.dtcitron.com
Preparing for the Physics GRE: Day 4
Advanced Topics: Atomic, Particle, and Nuclear Physics
Daniel T. Citron [email protected]
3/25/15 http://greprep.dtcitron.com
Atomic Physics
The$Periodic$Table$• A7few7things7worth7memorizing:7
• Fact:7Z7ranges7from717to7(about)71007
• Noble7gases,7in7order7by7weight7• Alkali7metals7
• Z7for7Carbon,7Iron7(as7well7as7H,7He)7
The$Hydrogen$Atom$• Most7complicated7system7completely7solved7by7quantum:7one7
electron7and7one7proton7
• Bohr7radius:7most7probable7distance7between7p7and7e7in7
hydrogen7ground7state7
• Allowed7energies,7where7n7is7the7quantum7number7of7the7
radial7state7of7the7atom:7
• It7is7worth7knowing7these7formulae7so7you7know7how7they7
scale7as7mass7or7charge7is7changed7(or7at7least7be7able7to7
reason7them7out7using7dimensional7analysis)77
Positronium$• ElectronOpositron7bound7state7• Mass7that7appears7in7H7
spectrum7is7reduced7eOp7mass:7
• Since7mp7>>7m
e,7the7reduced7
mass7is7set7to7me7
• But7for7positronium,7what7is7
the7new7reduced7mass?7
• How7does7the7energy7spectrum7change?7
• How7does7the7Bohr7radius7change?7
Spectrum$for$Hydrogen$$(and$for$Higher;Z$atoms)$
• Photons7are7emi"ed7when7atomic7electrons7fall7from7high7n7to7
low7n7states7
• Photon7energy7is7equal7to7the7energy7difference7between7the7two7energy7states7
• As7a7first7approximaVon,7can7treat7highOZ7atoms7as7having7
effecVve7charge7Ze7
16
Spectrum$for$Hydrogen$$(and$for$Higher;Z$atoms)$
• Long7wavelength7=>7small7frequency7
• nf7and7n
07must7be7close7to7one7another7
• Balmer7n07=73,7n
f7=72:7O5/367
• Lyman7n07=72,7n
f7=71:7O3/47
• Take7the7raVo…7
16
Ionization$energy$• How7much7energy7does7it7take7to7ionize7an7atom,7so7that7one7
(or7more)7electrons7are7removed7from7their7orbits7
completely?7
• Think7of7the7energy7required7as7an7atomic7transiVon7from7n07
to7nf7O>7∞:7
Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE.
16. A student makes 10 one-second measurements of the disintegration of a sample of a long-lived radioactive isotope and obtains the following values.
3, 0, 2, 1, 2, 4, 0, 1, 2, 5 How long should the student count to establish
the rate to an uncertainty of 1 percent? (A) 80 s (B) 160 s (C) 2,000 s (D) 5,000 s (E) 6,400 s
17. The ground state electron configuration
for phosphorus, which has 15 electrons, is
(A) 1s2 2s2 2p6 3s1 3p4 (B) 1s2 2s2 2p6 3s2 3p3 (C) 1s2 2s2 2p6 3s2 3d3 (D) 1s2 2s2 2p6 3s1 3d4 (E) 1s2 2s2 2p6 3p2 3d3
18. The energy required to remove both electrons
from the helium atom in its ground state is 79.0 eV. How much energy is required to ionize helium (i.e., to remove one electron) ? (A) 24.6 eV (B) 39.5 eV (C) 51.8 eV (D) 54.4 eV (E) 65.4 eV
19. The primary source of the Sun’s energy is a series of thermonuclear reactions in which the energy produced is c2 times the mass difference between (A) two hydrogen atoms and one helium atom (B) four hydrogen atoms and one helium atom (C) six hydrogen atoms and two helium atoms (D) three helium atoms and one carbon atom (E) two hydrogen atoms plus two helium atoms
and one carbon atom 20. In the production of X rays, the term
“bremsstrahlung” refers to which of the following?
(A) The cut-off wavelength, lmin , of the X-ray tube
(B) The discrete X-ray lines emitted when an electron in an outer orbit fills a vacancy in an inner orbit of the atoms in the target metal of the X-ray tube
(C) The discrete X-ray lines absorbed when an electron in an inner orbit fills a vacancy in an outer orbit of the atoms in the target metal of the X-ray tube
(D) The smooth, continuous X-ray spectra produced by high-energy blackbody radiation from the X-ray tube
(E) The smooth, continuous X-ray spectra produced by rapidly decelerating electrons in the target metal of the X-ray tube
21. In the hydrogen spectrum, the ratio of the
wavelengths for Lyman-a radiation (n = 2 to n = 1) to Balmer-a radiation (n = 3 to n = 2) is (A) 5/48 (B) 5/27 (C) 1/3 (D) 3 (E) 27/5
20
Helium$Ionization$Energy$
• The7energy7to7remove7two7He7electrons7equals7the7energy7
required7to7ionize7He7(remove7the7first)7plus7the7energy7
required7to7remove7the7second7
• Treat7ionized7Helium7as7a7hydrogenOlike7atom7with7Z7=727
• What7is7the7ionizaVon7energy7of7ionized7Helium?7
• 47*713.67eV7=754.47eV7• =>7797eVO54.47eV7=724.67eV7
Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE.
16. A student makes 10 one-second measurements of the disintegration of a sample of a long-lived radioactive isotope and obtains the following values.
3, 0, 2, 1, 2, 4, 0, 1, 2, 5 How long should the student count to establish
the rate to an uncertainty of 1 percent? (A) 80 s (B) 160 s (C) 2,000 s (D) 5,000 s (E) 6,400 s
17. The ground state electron configuration
for phosphorus, which has 15 electrons, is
(A) 1s2 2s2 2p6 3s1 3p4 (B) 1s2 2s2 2p6 3s2 3p3 (C) 1s2 2s2 2p6 3s2 3d3 (D) 1s2 2s2 2p6 3s1 3d4 (E) 1s2 2s2 2p6 3p2 3d3
18. The energy required to remove both electrons
from the helium atom in its ground state is 79.0 eV. How much energy is required to ionize helium (i.e., to remove one electron) ? (A) 24.6 eV (B) 39.5 eV (C) 51.8 eV (D) 54.4 eV (E) 65.4 eV
19. The primary source of the Sun’s energy is a series of thermonuclear reactions in which the energy produced is c2 times the mass difference between (A) two hydrogen atoms and one helium atom (B) four hydrogen atoms and one helium atom (C) six hydrogen atoms and two helium atoms (D) three helium atoms and one carbon atom (E) two hydrogen atoms plus two helium atoms
and one carbon atom 20. In the production of X rays, the term
“bremsstrahlung” refers to which of the following?
(A) The cut-off wavelength, lmin , of the X-ray tube
(B) The discrete X-ray lines emitted when an electron in an outer orbit fills a vacancy in an inner orbit of the atoms in the target metal of the X-ray tube
(C) The discrete X-ray lines absorbed when an electron in an inner orbit fills a vacancy in an outer orbit of the atoms in the target metal of the X-ray tube
(D) The smooth, continuous X-ray spectra produced by high-energy blackbody radiation from the X-ray tube
(E) The smooth, continuous X-ray spectra produced by rapidly decelerating electrons in the target metal of the X-ray tube
21. In the hydrogen spectrum, the ratio of the
wavelengths for Lyman-a radiation (n = 2 to n = 1) to Balmer-a radiation (n = 3 to n = 2) is (A) 5/48 (B) 5/27 (C) 1/3 (D) 3 (E) 27/5
20
Ionization$energy$• Generally,7ionizaVon7energy7is7highest7for7noble7gases,7lowest7for7alkali7metals7
h"p://en.wikipedia.org/wiki/IonizaVon_energy7
32
Orbitals$
h"p://chemistry.beloit.edu/Stars/pages/orbitals.html7
Orbitals$• Orbitals7are7denoted7by7their7quantum7numbers7
• n7is7the7radial7quantum7number,7determines7energy7eigenstate7
• l7is7the7azimuthal7quantum7number:70,71,72,7…7nO17
• m,is,the,magne0c,quantum7number:7Ol,7Ol+1,7…7lO1,7l7
• l7>707states7are72l+1Ofold7degenerate7• l,7m7=707states7are7spherically7symmetric:7nonzero7l,7m7states7
have7nonzero7angular7momentum7and7break7symmetry7
• For7each7n,7there7are7n27O7n7possible7states7to7fill7• We7disVnguish7these7angular7momentum7states7as7follows:7
• s:7l7=707(sharp)7• p:7l7=717(principal)7• d:7l7=727(diffuse)7• f:7l7=737(fundamental)7
How$ground$state$orbitals$are$Cilled$
• I7have7Z7electrons7in7an7atomic7ground7
state,7which7orbitals7do7they7fill?7
• NotaVon:7(n,7lOstate7label,7number7of7
electrons7in7state,7up7to72)7
• Filling7is7as7follows,7from7lei7to7right:77
71s272s272p673s273p674s273d107…7
• (Note,7for7example,7that74s7are7filled7
before73d)7
• Aier7Helium,7noble7gases7occur7when7pO
orbitals7are7filled:7
• He:71s2,77Ne:71s272s272p6,7• Ar:71s272s272p673s273p6,7etc.7
• SomeVmes7this7notaVon7is7abbreviated:7
• Ca:71s272s272p673s273p674s2=7Ar74s27
How$ground$state$orbitals$are$Cilled$• NotaVon:7(n,7lOstate7label,7number7of7electrons7in7state,7up7to72)7
7 71s272s272p673s273p674s273d1074p6,• (A)7What7about73d?7
• (B)7Only717electron7in74s7• (C)7No7l7=747electrons7here7• (D)7I7count7197orbitals7filled7• (E)7sOorbitals7have707net77777angular7momentum7and7are7
777spherically7symmetric7
7
Spectroscopic$notation$• There’s7yet7another7notaVon7for7the7state7of7atoms,7that7can7
also7account7for7states7above7the7ground7state7
• S7is7the7total7spin7momentum7of7the7electrons7
• Electrons7paired7together7in7the7same7state7have707net7spin7
• SpinOup7and7spinOdown7halfOshells7are7filled7separately7• That7is7to7say,7three7p7states7(px,7py,7pz)7are7filled7as7follows:7(1,0,0),7(1,1,0),7(1,1,1),7(1,1,2),7(1,2,2),7(2,2,2)7
• Only7unpaired7electrons7contribute7to7S7• L7is7the7lOstate7label7of7the7atom7(S,7P,7D,7F,7etc)7
• Each7halfOshell7is7filled7in7order:7l,7lO1,7lO2,7…71Ol,7Ol7• J7is7the7total7angular7momentum,7ranging7from7L+S7to7|LOS|7
• |LOS|7if7outermost7subshell7is7only7half7filled7
• L+S7if7outermost7subshell7is7completely7filled7
Spectroscopic$notation$• S7is7the7total7spin7momentum7of7the7electrons7
• Electrons7paired7together7in7the7same7state7have707net7spin7
• L7is7the7lOstate7label7of7the7atom7(S,7P,7D,7F,7etc)7
• Each7halfOshell7is7filled7in7order:7l,7lO1,7lO2,7…71Ol,7Ol7• J7is7the7total7angular7momentum,7ranging7from7L+S7to7|LOS|7
• |LOS|7if7outermost7subshell7is7only7half7filled7
• L+S7if7outermost7subshell7is7completely7filled7
• Examples:7
• Mg:71s272s272p673s27O>7s7=70,7l7=70,7j7=707=>77
• Example7of7an7atom7with7all7shells7filled7
• C:7He72p27O>7s7=71,7l7=717+70,7j7=7lOs7=707=>7
• F:7He72p57O>7s7=7½,7l7=71+0O1+1+07=71,7j7=7l+s7=73/27=>7
• P:7Ne73s273p37O>7s7=73/2,7l7=71+0O1=70,7j7=7lOs7=73/27=>7
Spectroscopic$notation$• Two7examples:7
• Note7the7atom7is7out7of7its7
ground7state7
• S7=73/27• l7=70+1+17=727
7
7
• Na:7Fill7up7to7117electrons:7• 1s272s272p673s17• l7=707• S7=7½7• J7=7|lOs|7
Selection$Rules$• For7a7hydrogenOlike7atom7to7undergo7a7transiVon7from7a7
higher7energy7state7to7a7lower7energy7state7(thus7emipng7a7
photon),7there7are7restricVons7on7the7transiVons7that7are7
allowed7
• Specifically,7the7angular7momentum7quantum7numbers7must7
change:7
• Δl7=7+17or7O17• Δm7=7+1,7O1,7or707
• When7working7in7spectroscopic7notaVon:7
• ΔJ7=7+1,7O1,7or707• Δs7=707(no7restricVons7due7to7spin,7outside7of7Pauli)7
• “Electric7dipole7transiVon”7
Selection$Rules$;$Examples$• Two7examples:77
• Spherically7symmetric7wave7funcVons7
are7both7SOtype7orbitals7
• There7must7be7some7change7in7angular7
momentum7for7radiaVon7to7occur7
• Need7to7use7spectroscopic7notaVon7here7as7well!7
• S7=71/2,7L7=71,7J7=7L+S7=73/27• (A)7Seems7possible7
• (B)7Angular7momentum7hasn’t7changed7
• (C)7Not7true7• (D)7An7electron7with7spin73/2?7• (E)7Need7an7n=47state7to7have7a7dOorbital7
32
Atomic$Physics$Summary$• Know7parts7of7the7periodic7table7• Understand7and7be7able7to7recognize7the7spectrum7and7
orbitals7of7hydrogenOlike7atoms7
• Be7able7to7calculate7spectrum7and7ionizaVon7energies7
• Know7the7order7in7which7orbitals7are7filled7• Recognize7spectroscopic7notaVon7• Remember7selecVon7rules7for7dipole7transiVons7
• Other7topics7• Basic7chemistry7
• Types7of7chemical7bonds7
• What7causes7spectra7to7change?7(Pressure,7Temperature,7etc.)7
Particle Physics
Some$Experimental$Context$• Where7do7“parVcles”7come7from?7
• RadioacVve7decay7(n,7e+,7etc)7• The7environment,7such7as7products7from7
Cosmic7Rays7(muons,7etc)7
• Accelerators,7such7as7the7LHC7(quarks,7etc)7• How7do7we7“see”7them?7
• Cloud7chambers7
• Bubble7chambers7
• ScinVllators7• How7do7we7measure7their7properVes?7
• InteracVons7with7ma"er7
• Indirectly7through7decay7products7
h"p://en.wikipedia.org/wiki/Cloud_chamber7
h"p://en.wikipedia.org/wiki/File:CERN_LHC_Tunnel1.jpg7
The$Standard$Model$
h"p://en.wikipedia.org/wiki/File:Standard_Model_of_Elementary_ParVcles.svg7
The$Standard$Model$• All7elementary,7nonOcomposite7parVcles7
that7we7know7of7(so7far)7
• Quarks7• 67flavors7• FracVonal7charge7• Fermions7
• Up/Down7make7up7protons,7neutrons7
• Leptons7• 37flavors7• Fermions7
• Electrons7and7heavier7electrons7• Neutrinos,7chargeless7and7(pracVcally)7massless7
• Force7Carriers7• Bosons7• Photons7–7carry7ElectromagneVc7Force7
• Gluons7–7carry7Strong7Nuclear7Force7• W/Z7–7carry7Weak7Nuclear7Force7
• (Probably7don’t7need7Higgs7physics7for7test)7
40
Conserved$Quantities$• Most7parVcle7physics7GRE7quesVons7deal7with7nuclear7
reacVons7and7other7types7of7decay7processes7
• Typically,7reacVons7obey7conserva0on,laws,• What7you7probably7already7know:7
• Momentum7and7Energy7
• Charge7• Angular7momentum7(spin)7
• New7concepts7from7parVcle7physics:7
• Lepton7Number7
• Baryon7Number7
• Other7quanVVes7violated7in7Weak7interacVons7only:7
• Strangeness7• Parity7• ChargeOParity7
Lepton$Number$• 37flavors7of7lepton7(electron,7muon,7tauon)7
• Note:7each7electronOlike7parVcle7has7a7corresponding7neutrino7with7the7same7flavor,7eg7muon7and7muon7neutrino7
• The7number7of7parVcles7belonging7to7each7flavor7of7lepton7is7
conserved7
• NB:7anVOparVcles7contribute7nega)ve7lepton7number7
• Example:7anVOelectrons7(e+)7have7electron7number7O17
007626-54721 • ETS/ GRE Practicing to Take the Lit in English Test • RI51621 • OC 5/9/01revs 5/18/01 rkc • revs 6/29/01 rKc* • revs 7/20/01 sb • pre!ight 8/10/01 chw • revs 5/16/02 jjh • revs 6/12/02 jjh • pre!ight 6/27/02 jjh • 1stRevs…3.5.04…kaj • pre!ight 04/01/04 mwr • dr01 4/22/10 mc • dr01revs 5/7/10 mc • pdf 5/10/10 mc • Drft02 5/20/10 jdb • Revs Drft02 5/26/10 jdb • PDF Drft002/5/26/10 jdb • Pre!ight 6/2/10 jdb • dr01 5/4/11 mc • RevsDrft01 5/12/11 jdb • PDF Drft01 5/12/11 jdb • Drft02 5/23/11 jdb • PDF Drft02 5/24/11 jdb • Pre!ight 6/6/11 jdb
80
Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE.
-72-
95. Let -̂ be a quantum mechanical angular momentum operator. The commutator
ˆ ˆ ˆ,x y xJ J JË ÛÍ Ý is equivalent to which of the following? (A) 0 (B) ˆ
zi J=
(C) ˆ ˆz xi J J=
(D) ˆ ˆx zi J J� =
(E) ˆ ˆx yi J J=
96. Which of the following ions CANNOT be
used as a dopant in germanium to make an n-type semiconductor? (A) As (B) P (C) Sb (D) B (E) N
97. In the Compton effect, a photon with energy E scatters through a 90q angle from a stationary electron of mass m. The energy of the scattered photon is (A) E
(B) 2E
(C) 2
2E
mc
(D) 2
2E
E mc�
(E) 2
2E mc
E mc¹�
98. Which of the following is the principal decay
mode of the positive muon P+ ?
(A) eeP Q� �� �
(B) p PP Q� � � �
(C) en eP Q� �� � �
(D) ee PP Q Q� �� � � �
(E)� e PP S Q Q� �� � � �
Lepton$Number$Example$• Need7to7conserve7charge7(doesn’t7eliminate7any7results)7
• Need7to7conserve7muon7number7and7electron7number:7
• (A)7O17mu7O>7O17e7+717e7
• (B)7O17mu7O>7proton?7+717mu7
• (C)7O17mu7O>7neutron?7O17e7+717e7
• (D)7O17mu7O>7O17e7+717e7O17mu7
• (E)7O17mu7O>7pion?7O717e7+717mu7
• AddiVonal7example:7
007626-54721 • ETS/ GRE Practicing to Take the Lit in English Test • RI51621 • OC 5/9/01revs 5/18/01 rkc • revs 6/29/01 rKc* • revs 7/20/01 sb • pre!ight 8/10/01 chw • revs 5/16/02 jjh • revs 6/12/02 jjh • pre!ight 6/27/02 jjh • 1stRevs…3.5.04…kaj • pre!ight 04/01/04 mwr • dr01 4/22/10 mc • dr01revs 5/7/10 mc • pdf 5/10/10 mc • Drft02 5/20/10 jdb • Revs Drft02 5/26/10 jdb • PDF Drft002/5/26/10 jdb • Pre!ight 6/2/10 jdb • dr01 5/4/11 mc • RevsDrft01 5/12/11 jdb • PDF Drft01 5/12/11 jdb • Drft02 5/23/11 jdb • PDF Drft02 5/24/11 jdb • Pre!ight 6/6/11 jdb
80
Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE.
-72-
95. Let -̂ be a quantum mechanical angular momentum operator. The commutator
ˆ ˆ ˆ,x y xJ J JË ÛÍ Ý is equivalent to which of the following? (A) 0 (B) ˆ
zi J=
(C) ˆ ˆz xi J J=
(D) ˆ ˆx zi J J� =
(E) ˆ ˆx yi J J=
96. Which of the following ions CANNOT be
used as a dopant in germanium to make an n-type semiconductor? (A) As (B) P (C) Sb (D) B (E) N
97. In the Compton effect, a photon with energy E scatters through a 90q angle from a stationary electron of mass m. The energy of the scattered photon is (A) E
(B) 2E
(C) 2
2E
mc
(D) 2
2E
E mc�
(E) 2
2E mc
E mc¹�
98. Which of the following is the principal decay
mode of the positive muon P+ ?
(A) eeP Q� �� �
(B) p PP Q� � � �
(C) en eP Q� �� � �
(D) ee PP Q Q� �� � � �
(E)� e PP S Q Q� �� � � �
Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE.
74. The Lagrangian for a mechanical system is
L aq bq �� ,2 4
where q is a generalized coordinate and a and b are constants. The equation of motion for this system is
(A) �q ba
q 2
(B) �q ba
q 2 3
(C) ��q ba
q � 2 3
(D) ��q ba
q � 2 3
(E) ��q ba
q 3
!!!
F
HGGI
KJJ = "L
NMMM
O
QPPP
F
HGGI
KJJ
aaa
aaa
x
y
x
y
z
1 2 3 2 03 2 1 2 00 0 1
/ // /
z
75. The matrix shown above transforms the com-ponents of a vector in one coordinate frame S to the components of the same vector in a second coordinate frame S!. This matrix represents a rotation of the reference frame S by
(A) 30° clockwise about the x-axis (B) 30° counterclockwise about the z-axis (C) 45° clockwise about the z-axis (D) 60° clockwise about the y-axis (E) 60° counterclockwise about the z-axis
76. The mean kinetic energy of the conduction
electrons in metals is ordinarily much higher than kT because (A) electrons have many more degrees of
freedom than atoms do (B) the electrons and the lattice are not in thermal
equilibrium (C) the electrons form a degenerate Fermi gas (D) electrons in metals are highly relativistic (E) electrons interact strongly with phonons
77. An ensemble of systems is in thermal equilibrium with a reservoir for which kT = 0.025 eV. State A has an energy that is 0.1 eV above that of state B. If it is assumed the systems obey Maxwell-Boltzmann statistics and that the degeneracies of the two states are the same, then the ratio of the number of systems in state A to the number in state B is
(A) e+4
(B) e+0.25
(C) 1 (D) e�0.25
(E) e�4
78. The muon decays with a characteristic lifetime
of about 10�6 second into an electron, a muon neutrino, and an electron antineutrino. The muon is forbidden from decaying into an electron and just a single neutrino by the law of conservation of (A) charge (B) mass (C) energy and momentum (D) baryon number (E) lepton number
79. A particle leaving a cyclotron has a total
relativistic energy of 10 GeV and a relativistic momentum of 8 GeV/c. What is the rest mass of this particle?
(A) 0.25 GeV/c2 (B) 1.20 GeV/c2
(C) 2.00 GeV/c2 (D) 6.00 GeV/c2 (E) 16.0 GeV/c2
50
Baryons$• Composite7parVcles7made7up7of73,quarks,• Examples:7
• Proton7=727up7+717down7• Neutron7=727down7+717up77• Most7ma"er7consists7of7baryons7
• All7baryons7are7fermions,• Baryon7number7=7(number7of7quarks7–7number7of7anVquarks)/37
• So7protons7and7neutrons7have7B7=7+17• AnVOprotons7have7B7=7O17
• Other7(more7exoVc7examples)7
• Δ7(37up/down7quarks)7• Λ,7Σ7(27up/down7quarks)7• Ξ7(17up/down7quark)7• Ω7(07up/down7quarks)7
…$as$opposed$to$Mesons$• Composite7parVcles7made7up7of7one7quark7and7one7anVquark77
• These7parVcles7appear7as7decay7products7(for7example7from7
cosmic7rays)7
• Examples:7
• Pions:7π+7πO7π0,7consist7of7up/down7quarks7
• Kaons:7K+7KO7K07,7consist7of7one7up/down7quark,7one7strange7quark7• Baryon7number7is707
• (Side7note:7Older7literature7may7refer7to7muons7as7mesons,7
though7now7we7know7they7are7leptons.)7
The$Weak$Interaction$• Interacts7with7all7fermions7
• Mediated7by7Z,7W+,7WO7bosons7
• Responsible7for7all7decay7of7subatomic7parVcles7
• Produces7a7whole7zoo7of7possible7interacVons7
• Certain7symmetries7are7violated7by7
Weak7InteracVons:7
• Quarks,change,flavor,• Parity7(also7chargeOparity)7
• Example:7Beta7decay7
• Nuclear7scale:7nO>7p+7+7eO7O7νe7
• SubOnuclear7(quark)7scale:77777777777777dO>7u7+7eO7O7ν
e7
007626-54721 • ETS/ GRE Practicing to Take the Lit in English Test • RI51621 • OC 5/9/01revs 5/18/01 rkc • revs 6/29/01 rKc* • revs 7/20/01 sb • pre!ight 8/10/01 chw • revs 5/16/02 jjh • revs 6/12/02 jjh • pre!ight 6/27/02 jjh • 1stRevs…3.5.04…kaj • pre!ight 04/01/04 mwr • dr01 4/22/10 mc • dr01revs 5/7/10 mc • pdf 5/10/10 mc • Drft02 5/20/10 jdb • Revs Drft02 5/26/10 jdb • PDF Drft002/5/26/10 jdb • Pre!ight 6/2/10 jdb • dr01 5/4/11 mc • RevsDrft01 5/12/11 jdb • PDF Drft01 5/12/11 jdb • Drft02 5/23/11 jdb • PDF Drft02 5/24/11 jdb • Pre!ight 6/6/11 jdb
50
Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE.
-42-
61. A particle with mass m and charge q , moving with a velocity v, enters a region of uniform magnetic field B, as shown in the figure above. The particle strikes the wall at a distance d from the entrance slit. If the particle’s velocity stays the same but its charge-to-mass ratio is doubled, at what distance from the entrance slit will the particle strike the wall? (A) 2d
(B) 2d
(C) d
(D) 12
d
(E) 12 d
62. Consider the closed cylindrical Gaussian surface above. Suppose that the net charge enclosed within this surface is +1 u 10�9 C and the electric flux out through the portion of the surface marked A is �100 N!m2/C. The flux through the rest of the surface is most nearly given by which of the following?
(A) �100 N!m2/C (B) 0 N!m2/C (C) 10 N!m2/C (D) 100 N!m2/C (E) 200 N!m2/C
13N o 13C + e+ + Qe
63. The nuclear decay above is an example of a process induced by the (A) Mössbauer effect (B) Casimir effect (C) photoelectric effect (D) weak interaction (E) strong interaction
Weak$Interaction$Example$
• (A)7Pions7are7mesons,7not7leptons7
• (B)7Weak7interacVons7only7affect7fermions7(Λ7and7p7have7spin7½)7
• (C)7Only7need7neutrinos7to7conserve7lepton7number,7not7necessary7
for7every7weak7interacVon7
• (D)7Looks7like7angular7momentum7is7conserved7• (E)7Strangeness7counts7number7of7strange7quarks.77Since7quarks7can7
change7flavor7under7weak7interacVons,7this7could7be7right7
Strong$Interaction$• Responsible7for7holding7quarks7together77• Hadrons:7includes7mesons7and7baryons7
• Mediated7by7gluons7
• “Massive7photons”7follow7the7Yukawa7potenVal7
• (Same7as7chargeOscreened7potenVal7for7electrons7in7ma"er)7
How$do$particles$interact$with$matter?$• Treat7the7interacVon7between7incident7parVcles7and7ma"er7
probabilisVcally,7with7some7probability7of7sca"ering7occurring7
• Probability:7Cross7secVons7are7measured7in7units7of7area,• Not7totally7necessary7to7memorize7rules7for7cross7secVons,7but7
can7list7some7rules7of7thumb7that7build7on7physical7intuiVon7
• Charged7parVcles7interact7with7electrons7in7ma"er,7so7the7higher7
Z7of7the7ma"er,7the7more7likely7they7are7to7interact7
• Lighter7parVcle7mass7sca"er7more7easily7(less7inerVa7=>7easier7to7
change7momentum)7
How$do$photons$interact$with$matter?$
• Photons7primarily7interact7
with7atomic7electrons7
• Three7primary7processes7
(which7you7need7to7know7for7the7test)7
• Compton7Sca"ering7
• Photoelectric7effect7• Pair7producVon7
• Important7to7know:7
• Why7does7the7photoelectric7
effect7only7occur7with7atomic7
electrons7(as7opposed7to7
free)?7
• Why7can’t7pair7producVon7
occur7in7vacuum?7
7
Particle$Physics$Summary$• Begin7with7the7Standard7Model7
• Know7the7different7properVes7of7fundamental7parVcles7
• What7quanVVes7are7conserved?7
• Charge,7spin7angular7momentum7
• Lepton7number7
• Baryon7number7
• Weak7interacVons7
• Interacts7with7fermions7
• Mediates7parVcle7decay7
• Quarks7can7change7flavor7• InteracVons7between7parVcles7and7ma"er7
• Other7topics:7• AddiVonal7symmetries:7Parity,7ChargeOparity7
• Zoo7of7subatomic7mesons7and7baryons7
• InteracVon7cross7secVons7
Nuclear Physics
Notation$• Atomic7nucleus7consists7of7protons7and7neutrons7
• A7nucleus7of7X7has7Z7protons7and7A7total7nucleons7(n7+7p)77
7
• For7small7nuclei,7same7number7of7neutrons7as7protons,7A7=727Z7
• For7large7nuclei7(and7isotopes)7the7number7of7neutrons7may7
vary7
• Example:7
• Ordinary7Carbon:767protons,767neutrons,7127nucleons7• CarbonO14:767protons,787neutrons,7147nucleons7
Radioactive$Decay$Modes$• Alpha7decay:7the7nucleus7emits7a7Helium7nucleus7
7
• Beta7decay:7the7nucleus7emits7an7electron7and7anVneutrino7
7
• Gamma7decay:7the7nucleus7emits7a7photon7(loses7some7
energy,7but7does7not7change7otherwise)7
• Deuteron7decay7(very7rare):777777the7nucleus7emits7a7deuteron7
7
7
7
• An7example7problem7O>7
Radioactive$Decay$Modes$Example$
• Alpha7decay7takes7away747nucleons7and727protons7(AO>AO4,7ZO>ZO2)7• Beta7decay7adds7one7proton7(Z7O>7Z+71)7• Beta7decay7followed7by7alpha7decay:7AO>7AO4,7ZO>7ZO17• If7you7don’t7remember7the7details7of7beta7decay,7how7do7you7know7
whether7(A)7or7(B)7is7correct?7
7
Nuclear$Binding$Energy$• Nucleons7repel7electromagneVcally,7but7are7bound7in7place7by7
the7Strong7force7
• Can7define7a7binding7energy7per7nucleon,7varies7with7size7• Iron7(Z7=726)7has7max7energy7per7nucleon7
• Much7larger7nuclei7are7so7big7that7the7strong7force7has7smaller7
effect7
40
h"p://en.wikipedia.org/wiki/File:Binding_energy_curve_O_common_isotopes.svg7
Radioactivity$• RadioacVve7substances7break7down7over7Vme7
• The7process7occurs7at7random,7but7we7can7model7what7
fracVon7N7radioacVve7atoms7will7break7down7
• The7change7in7the7number7of7radioacVve7atoms7(ie,7the7atoms7
that7undergo7decay)7in7Vme7dt7is7proporVonal7to7the7number7
of7atoms7N:7
• Solving,7we7find7exponenVal7decay:7
• RadioacVve7halfOlife7is7the7Vme7required7for7half7of7the7N7
atoms7to7decay7(an7invariant,7since7the7decay7process7is7
exponenVal)7
Radioactivity$• How7do7halfOlives7add?7• Think:7there7are7two7processes7that7are7contribuVng7to7the7
disappearance7of7the7material7
• Total7halfOlife7must7be7smaller7
than7either7of7the7halfOlives7of7
the7individual7decay7processes7
• 1/t7is7the7rate7at7which7half7of7the7material7disappears7
• The7rates7add:,
Unauthorized copying or reuse of any part of this page is illegal. GO ON TO THE NEXT PAGE.
63. The distribution of relative intensity � �I l of blackbody radiation from a solid object versus the wavelength l is shown in the figure above. If the Wien displacement law constant is 2.9 � 10�3 m!K, what is the approximate temperature of the object? (A) 10 K (B) 50 K (C) 250 K (D) 1,500 K (E) 6,250 K
64. Electromagnetic radiation provides a means to
probe aspects of the physical universe. Which of the following statements regarding radiation spectra is NOT correct? (A) Lines in the infrared, visible, and ultraviolet
regions of the spectrum reveal primarily the nuclear structure of the sample.
(B) The wavelengths identified in an absorption spectrum of an element are among those in its emission spectrum.
(C) Absorption spectra can be used to determine which elements are present in distant stars.
(D) Spectral analysis can be used to identify the composition of galactic dust.
(E) Band spectra are due to molecules.
C kN hvkTA
hv kT
hv kT FH IK �3
1
2
2e
(e
/
/ )
65. Einstein’s formula for the molar heat capacity C of solids is given above. At high temperatures, C approaches which of the following? (A) 0
(B) 3kN hvkTAFH IK
(C) 3kN hvA (D) 3kNA (E) N hvA
66. A sample of radioactive nuclei of a certain element
can decay only by g -emission and b -emission. If the half-life for g -emission is 24 minutes and that for b -emission is 36 minutes, the half-life for the sample is (A) 30 minutes (B) 24 minutes (C) 20.8 minutes (D) 14.4 minutes (E) 6 minutes
67. The 238U nucleus has a binding energy of about
7.6 MeV per nucleon. If the nucleus were to fission into two equal fragments, each would have a kinetic energy of just over 100 MeV. From this, it can be concluded that
(A) 238U cannot fission spontaneously (B) 238U has a large neutron excess (C) nuclei near A = 120 have masses greater than
half that of 238U (D) nuclei near A = 120 must be bound by about
6.7 MeV/nucleon (E) nuclei near A = 120 must be bound by about
8.5 MeV/nucleon
46
Nuclear$Physics$Summary$• Recognize7the7notaVon7used7• RadioacVve7decay7processes7• Nuclear7binding7energy7• RadioacVve7halfOlife7• Other7topics:7• Examples7of7radioacVve7decays7
• Fusion,7as7in7stars7
Other$Topics$• Laboratory7methods7
• Reading7logOlog7and7semilog7graphs7
• Reading7oscilloscope7screens7• Precision7vs.7accuracy7• StaVsVcs7–7sampling,7adding7uncertainVes7
• Band7theory7of7solids7• Valence7and7conducVon7bands7• Conductors,7insulators,7semiconductors7
• Fluid7staVcs7• Incompressibility7–7flux7conservaVon7
• Buoyant7forces7• Streamline7equaVon:7
