Question

A particle with rest mass 2.4 X 10-28 kg is moving with speed 2.4 X108 m/s. It is found that this particle decays into two photons. Find: (a) the frequency and wavelength of these photons, (b) angle between these two outgoing photons. ​

Answer 1

Answer:

Solved Problems in Special Relativity

Charles Asman, Adam Monahan and Malcolm McMillan

Department of Physics and Astronomy

University of British Columbia,

Vancouver, British Columbia, Canada

Fall 1999; revised 2011 by Malcolm McMillan

Given here are solutions to 24 problems in Special Relativity.

The solutions were used as a learning-tool for students in the introductory undergraduate course Physics

200 Relativity and Quanta given by Malcolm McMillan at UBC during the 1998 and 1999 Winter Sessions.

The solutions were prepared in collaboration with Charles Asman and Adam Monaham who were graduate

students in the Department of Physics at that time.

The problems are from Chapter 1 Relativity of the course text Modern Physics by Raymond A. Serway,

Clement J. Moses and Curt A. Moyer, Saunders College Publishing, 2nd ed., (1997).

Standard Inertial Frames

We use the standard inertial frames S and S

0 which are set up such that the x and x

0 axes coincide and

the y and y

0 axes and z and z

0 axes are parallel. Seen from S, S

0 moves in the positive x-direction with speed

v and, seen from S

0

, S moves in the negative x

0

-direction with speed v. Furthermore, it is imagined that in

each inertial frame there is an infinite set of recording clocks at rest in the frame and synchronized with each

other. Clocks in both frames are set to zero when the origins O and O0

coincide.

Time Dilation (“Moving Clocks Run Slow”)

Problem 1.6, page 45

•At what speed does a clock move if it runs at a rate which is one-half the rate of a clock at rest?

Solution

We assume that the clock is at rest in S

0

. As observed by stationary observers in S, the clock moves in the

positive x-direction with speed v. Text Eq. (1.30):

t = γ

t

0 +

vx0

c

2

(1)

relates the time t measured in S with the time t

0 measured in S

0 where

γ =

1

p

1 − β

2

(2)

and

β = v/c (3)