E
  mc E 2 
(pc) 2 
(mc ) K
  mc 2  mc 2 p
  mv p


E / c, p , p , p z

  pc
E
S
2 
(E
1

E )
2  c (p
1
 p )
2
Example 2.1
a. The Relativistic Heavy Ion Collider (RHIC) at Brookhaven is colliding fully ionized gold (Au) nuclei accelerated to energy 200 GeV per nucleon. Each Au nucleus contains 197 nucleons. What is the speed and momentum of each Au nucleus just before collision? b. A proton with rest energy of 938 MeV has a total energy of 1400 MeV. What is its speed and momentum of the proton?
Example 2.2
A Lambda-particle (

) is a subatomic particle which decays into a proton (p) and a pion
(

); that is
 → p + 
. In a certain experiment the outgoing momentums for the proton and pion are observed to be in the same direction along the x-direction, and with values of p p
= 581 MeV/c and p

= 140 MeV/c. (Hint: m p
= 938 MeV and m

= 140 MeV) a. Sketch a picture of the collision. Which particle is moving faster after the Λ decays, the proton or the pion? b. Find the rest energy of the

-particle?

Example 2.3
The positive pion decays from rest into a muon and a neutrino,

+ → 
+ +


. (Hint: m

=
106 MeV/c 2 , m

= 140 MeV/ c 2 and m
ν
≅ 0) a. Sketch a picture of the collision. Using the given values, is the muon relativistic or nonrelativistic? b. Use conservation of energy and momentum to determine the speed of the muon.
Example 2.4
An electron-positron pair combined as positronium is at rest in the laboratory. (a) The pair annihilate, producing a pair of photons moving in opposite directions in the lab.
Show that the invariant rest energy of the photons is equal to that of the electron pair.
(b) What if ortho-positronium is produced, where three photons are produced instead.
What is the energy of each of the photons?
Example 2.5
Find the minimum energy a gamma ray must have to initiate the reaction

+ p
  0 + p if the target proton is at rest.