Problem 1:

HEPA is an asymmetric electron proton collider located near the city of Hamburg in Germany.  The energy of the electron beam is 26 GeV and the energy of the proton beam is 820 GeV.  Ignore baryon and lepton number conservation and calculate
(a)  the maximum number of neutral pions (mass of p⁰ = 134.98 MeV) that can be produced in one proton-electron collision.
(b)  What momentum would a beam of electrons incident on protons at rest need to have to produce the same number of pions as in part (a)

Problem 2:

A pion (p) decays at rest into a muon (m) and a neutrino (n).  In terms of the masses m_p and m_m (use the approximation m_n = 0), find:
(a)  the momentum, energy, and velocity of the outgoing muon.
(b)  In the rest frame of the outgoing muon, what is the energy of the neutrino?  What was the initial velocity of the pion in this frame?

Problem 3:

A f particle (m_f = 1.020GeV/c²) has a momentum of 3GeV/c along the z-axis in the laboratory frame. 
It decays f ® K⁺K^- into two charged kaons (m_K⁺ = m_K^- = 0.494GeV/c² ).
(a)  Calculate the momentum P_K of each kaon in the laboratory frame if the decay axis coincides with the z-axis.
(b)  Calculate the momentum P_K of each kaon in the laboratory frame if the decay axis is perpendicular to the z-axis.

Problem 4:

In the following, two examples of a decaying system are presented, where the decay products travel with velocities comparable to the speed of light c.
1. Two electrons are ejected simultaneously in opposite directions from an atom.  Each electron has a speed as measured by a laboratory observer of 0.5c.  What is the speed of one electron as seen from the rest frame of the other electron
(a)  in the classical approach?
(b)  in the relativistic approach?
Distinguish carefully the velocities in the respective frames.

2. The neutral pi meson, p°, has a rest mass of 135 MeV/c².  It decays into two photons (g rays) of equal energy and opposite direction in its rest frame.  In the laboratory frame the p° is moving with a total energy 25% larger than its rest energy.
(a)  What are the energies of the g rays, as measured in the laboratory, if the decay process causes them to be emitted in opposite directions along the pion's original line of motion?
(b)  What is the velocity of each g rays as observed by the other?

Problem 5:

A reference frame K' is moving with uniform velocity v = vi with respect to reference frame K.
(a)  In K, a plane wave with angular frequency w is traveling in the i direction. What is its frequency in K'?
(b)  In K, a plane wave with angular frequency w is traveling in the j direction. What is its frequency in K'?
(c)  In K, a plane wave with angular frequency w is traveling in a direction making an angle of 45^o with respect to the i direction and the j direction. What is its frequency in K'?

Problem 6:

A, located on earth, signals with a laser pulse every six minutes.  B is on a space station that is stationary with respect to earth.  C is in a rocket traveling from A to B with a velocity v = 0.6c relative to A.

(a)  At what intervals does B receive signals from A?
(b)  At what intervals does C receive signals from A?
(c)  If C sends light pulses back to A, at what intervals does A receive these pulses?

Problem 7:

A source emits electromagnetic waves with frequency f into a 4p solid angle.  What is the frequency f' of the waves observed by an observer moving with speed v in a circular orbit around the source?