Each part of a multipart question is of equal weight.
Show your work and reasoning; part marks will be given.
Useful information is given on the last two pages of this exam.
* Some of the following numerical constants may be useful:
pi | p= 3.14159265358979323… | |
speed of light | c = 299792458 m s^{-1} | |
Planck's constant, reduced | h/2p = 6.58212x10^{-22} MeV s | |
conversion constants | hc/2p = 197.327 MeV fm | (hc/2p)^{2} = .389379 GeV^{2} mb |
conversion factors | 1 eV = 1.602177x10^{-19} J | 1 eV/c^{2} = 1.782662x10^{-36} kg |
1 barn = 10-24 cm^{2} | ||
unified atomic mass unit | u = 931.494 MeV/c^{2} | |
Avogadro's constant | N_{A} = 6.022137x10^{23} mol^{-1} | |
electron charge | e = 1.602x10^{-19} C | |
electron magnetic moment | µ_{e} = 2.9665x10^{-7} eV^{-1} | |
Boltzmann constant | k = 8.617x10^{-5} eV/Kelvin | |
fine structure constant | a= 1/137.0360 | |
strong coupling constant | a_{S}(M_{Z})= 0.118±0.003 | |
Cabibbo angle | sin q_{c} @ V_{us} = 0.22 | |
weak mixing angle | sin^{2}q_{W}= 0.2315 | |
standard grav. accel., sea level | g = 9.8 m/s^{2} | |
Hubble constant | H0=0.1 Gyr^{-1} | |
neutral kaon mass difference | m_{KL}- m_{KS}_{ }= 3.510±0.018 meV | |
Fermi weak coupling constant | G_{F} = 1.166x10^{-5} GeV^{-2} | |
Newton's (gravitational) constant | = 6.707x10^{-39} GeV^{-2} | |
Z^{0} branching fractions | B.R.(Z^{0}->e^{+}e^{-})=3.21±0.07% | B.R.(Z^{0}->hadrons) = 71±1% |
* Particle Properties *
Boson | (GeV/c^{2}) | Lepton | (MeV/c^{2}) | Lifetime | (GeV/c^{2}) | |||
Hadron | Quark Content | Mass (MeV/c^{2}) | I(J^{PC}) |
p^{0} | (u-d)/2^{1/2} | 134.97 | 1(0^{-+}) |
p^{+}, p^{-} | u, d | 139.57 | 1(0^{-}) |
K^{+},K^{-} | u, s | 493.65 | |
K^{0}, anti-K^{0} | d, s | 497.67 | |
r^{+}, r^{0}, r^{-} | u, (u-d)/2^{1/2}, d | 770 | 1(1^{--}) |
p | uud | 938.27 | |
n | udd | 939.57 | |
L | uds | 1115.6 | 0(^{1}/_{2}^{+}) |
S^{0} | uds | 1192.6 | 1(^{1}/_{2}^{+}) |
D^{-}, D^{0}, D^{+}, D^{++} | ddd, udd, uud, uuu | 1232 | ^{3}/_{2} (^{3}/_{2}^{+}) |
D^{0}, anti-D^{0} | u, c | 1863 | ^{1}/_{2} (0^{-}) |
D^{+},D^{-} | d, c | 1869 | ^{1}/_{2} (0^{-}) |
L_{c} | udc | 2285 | 0(^{1}/_{2}^{-}) |
B^{+},B^{-} | u, b | 5279 | ^{1}/_{2} (0^{-}) |
L_{b} | udb | 5640±50 | 0(^{1}/_{2}^{+}) |
Nuclei | Mass (in u) | Nuclei | Mass (in u) | Nuclei | Mass (in u) | ||
H^{1} | 1.007825 | _{2}He^{3} | 3.01603 | _{26}Fe^{56} | 55.934939 | ||
_{1}H^{2} | 2.0140 | _{2}He^{4} | 4.00260 | _{82}Pb^{208} | 207.976627 | ||
_{1}H^{3} | 3.01605 | _{6}C^{12} | 12 |
Problem 1
(a) An electron accelerator is to be designed to study properties of linear dimensions of 1 fm. What kinetic energy is required?
(b) What is the magnetic moment of a hydrogen atom?
Problem 2
This is a sketch of a very rare two-body decay of a neutral particle.
The sketch has been reduced and a scale provided.The two particle
tracks shown lie in the plane of the paper; the initial angle
between the two tracks at the decay point is 90°. There is
a magnetic field of 3.33 Tesla (33,333 Gauss) perpendicular to
the page. What is the mass of the unknown particle? (You don't
need to calculate the uncertainty in the mass.)
Problem 3
Explain how Rutherford's alpha-gold scattering data showed that
the electric charge in atoms is not uniformly distributed over
the entire volume of the atom.
A isospin I=1 meson is observed to decay into 3 pions but not
into 2 pions. (a) Is the weak interaction responsible for
this decay? (b) What is the strangeness of the charged
meson?