Environmental Engineering Reference
In-Depth Information
10
15
Hz travels at an angle of 20
◦
relative
to the positive
x
-axis. What angle does the photon make with the positive
x
-axis according to an observer who travels along the positive
x
-axis at
a speed of 0
.
87
c
? What is the frequency of the photon according to this
observer?
12.8 In the laboratory frame, a
φ
particle (mass 1020 MeV/
c
2
) travels in the
direction of the unit vector
n
with a momentum of 3000 MeV/
c
.Aftera
time it decays into two kaons, each of mass 494 MeV/
c
2
12.7 A photon of frequency 2
.
0
×
and each also
travelling in the
n
direction.
(a) What are the energy and momentum of each kaon in the rest frame of
the
φ
particle?
(b) The laboratory frame is moving with velocity
v
relative to the rest frame
of the
φ
particle. In which direction is
v
and what is its magnitude?
(c) Perform a Lorentz transformation on the kaon momenta obtained in part
(a) in order to deduce the momentum of each kaon in the laboratory
frame.
12.9 A
π
+
meson (mass 140 MeV/
c
2
) collides with a neutron (mass 940 MeV/
c
2
)
to produce a
K
+
meson (mass 494 MeV/
c
2
) and a
hyperon (mass
1115 MeV/
c
2
).
What is the minimum energy of the
π
+
meson for the reaction to proceed
in the frame in which the neutron is at rest?
12.10 A
K
meson (mass 498 MeV/
c
2
) is travelling through the laboratory when it
decays into two
π
mesons (each of mass 140 MeV/
c
2
). One of the
π
mesons
is produced at rest. What is the energy of the other?
12.11 In its rest frame, a
π
0
meson decays isotropically into two photons. If one
such meson is moving in the laboratory frame with a speed
u
show that the
probability of a photon being emitted into the solid angle d
is given by
u
c
2
1
−
d
P
d
1
4
π
=
c
cos
θ
2
,
1
u
−
where
θ
is the photon angle relative to the meson's direction of travel as
measured in the laboratory frame.
