Concepts in Physics - Week 16
WORKSHOP QUESTIONS
1.
The properties of the up, down and strange quarks and their
antiquarks are listed below:
quark
u
d
s
u
d
s
Electrical charge
+2/3
-1/3
-1/3
-2/3
+1/3
+1/3
strangeness
0
0
-1
0
0
+1
(a) List the nine possible quark-antiquark pairings with their charge
and strangeness properties.
(b) Construct an Eightfold Way chart with your results, and compare
it with the meson octet given in the lecture.
2.
(a) Calculate the Planck length by combining the fundamental
constants  , G (Newton’s gravitational constant) and c (the speed of
light).
(b) This “Planck length” provides a fundamental limit to the finescale structure of matter. What energy must an electron have to be
sensitive to structure at this scale?
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Concepts in Physics - Week 16
WORKSHOP SOLUTIONS
1. Note how the fractional quark charges add up to integers, agreeing with
observations!
Quarks:
S = +1:
S=0:
dsbar
Dubar
S = -1:
usbar
uubar
udbar
subar

sdbar

q = -1

q=0
q = +1
Mesons:
K0
S = +1:
S=0:
S = -1:
K+
-
0,,’
+
K-
K0 bar


q = -1

q=0
q = +1
2. (a) Dimension of [G] = [energy].[distance]/[mass] 2 = kg. m2.s-2 m.kg-2
= kg-1 m3 s-2 .
[hbar] = [energy].[time] = kg. m2.s-1.
[c] = m.s-1
So hbar.G has no mass in it : [hbar.G] = m5 s-3 .
Dividing by c3 eliminates the time dimension, leaving length squared. Thus the Planck
length is
G
c3
 10 35 m.
(b) If the electron wavelength is 10-35 m, then its momentum is p = h/  10 kg.m/s.
By special relativity p = (v)mv ~ mc, so that the electron’s energy is E=mc2 ~
3x109 J ~ 2x1028 eV. This would take some accelerator!
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