UNIVERSITY OF TORONTO

Midterm Test

PHY 357S

Duration - 50 Minutes

Allowed aids: Calculator and 1 letter-sized double-sided hand-written aid sheet.

Do 3 of 4 questions; each question has equal weight.

If you do all 4 questions, your best 3 marks will be used.

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:

pip= 3.14159265358979323…
speed of lightc = 299792458 m s-1
Planck's constant, reducedh/2p = 6.58212x10-22 MeV s
conversion constantshc/2p = 197.327 MeV fm (hc/2p)2 = .389379 GeV2 mb
conversion factors1 eV = 1.602177x10-19 J 1 eV/c2 = 1.782662x10-36 kg
1 barn = 10-24 cm2
unified atomic mass unitu = 931.494 MeV/c2
Avogadro's constant NA = 6.022137x1023 mol-1
electron chargee = 1.602x10-19 C
electron magnetic moment µe = 2.9665x10-7 eV-1
Boltzmann constantk = 8.617x10-5 eV/Kelvin
fine structure constant a= 1/137.0360
strong coupling constant aS(MZ)= 0.118±0.003
Cabibbo angle sin qc @ Vus = 0.22
weak mixing anglesin2qW= 0.2315
standard grav. accel., sea level g = 9.8 m/s2
Hubble constantH0=0.1 Gyr-1
neutral kaon mass difference mKL- mKS = 3.510±0.018 meV
Fermi weak coupling constant GF = 1.166x10-5 GeV-2
Newton's (gravitational) constant
GN = 6.673x10-11m3kg-1s-2
= 6.707x10-39 GeV-2
Z0 branching fractions B.R.(Z0->e+e-)=3.21±0.07% B.R.(Z0->hadrons) = 71±1%

Continued on page 3

 

 

* Particle Properties *

Boson
Mass
(GeV/c2)
Lepton
Mass
(MeV/c2)
Mean
Lifetime
Quarks
mass
(GeV/c2)
g
<3¥10-36
ne
<10-5
 
u
~0.005
gluon
<0.01
e-
0.510999
>4.3¥1023 y
d
~0.01
W±
80.22
nµ
<0.27
 
c
1.0-1.5
Z0
91.187
µ-
105.658
2.197 µs
s
0.1-0.3
H0
>58
nt
<10
 
t
174±6
graviton
~0
t-
1777
0.29 ps
b
~4.5

HadronQuark Content Mass (MeV/c2)I(JPC)
p0 (u-d)/21/2134.97 1(0-+)
p+, p- u, d139.571(0-)
K+,K-u, s 493.65
K0, anti-K0d, s 497.67
r+, r0, r- u, (u-d)/21/2, d770 1(1--)
puud938.27
nudd939.57
Luds 1115.60(1/2+)
S0 uds1192.61(1/2+)
D-, D0, D+, D++ ddd, udd, uud, uuu1232 3/2 (3/2+)
D0, anti-D0u, c 18631/2 (0-)
D+,D-d, c 18691/2 (0-)
Lc udc22850(1/2-)
B+,B-u, b 52791/2 (0-)
Lb udb5640±500(1/2+)

NucleiMass (in u) NucleiMass (in u) NucleiMass (in u)
H11.007825 2He3 3.0160326Fe56 55.934939
1H22.0140 2He4 4.0026082Pb208 207.976627
1H33.01605 6C12 12

Continued on page 4

 

 

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.

Problem 4

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?

This is the last page of this test.

 

 

Copyright 1998 David Bailey, University of Toronto