Question

1a: ​A negative pion ( ) is a particle that​ ​has a mass equal to 2.49 x 10​-28​ kg. What is the rest π− energy of the pion in joules and in megaelectron-volts (MeV)?





2b: ​A negative pion is observed to be moving to the right at 0.950​c ​ .​ ​ What is the negative pion’s total energy (in MeV) ​and ​ momentum at this speed?











3c: ​The negative pion decays (splits) into two particles, a muon ( ) and a neutrino ( ). The μ υ muon has a rest energy of 106 MeV, and the neutrino is (virtually) massless. After the decay, the total energy of the neutrino is observed to be 187 MeV. How much total energy must the ​muon ​ have?





4d: ​ At what speed is the muon observed to be travelling?

Answer 1

1a. Rest mass energy

where m0 = rest mass = 2.49* 10-28 kg

c= speed of light = 3*108 m/sec

E0 = 2.49*10-28*9*1016J= 22.41*10-12J = 22.41*10-12/(1.6*10-19) eV = 14.006*107 eV = 140.06 MeV

because 1 eV = 1.6*10-19 J, and 1 Mev = 106 eV.

2b.

Total energy = kinetic energy + rest mass energy

E = KE+ E0

where v = 0.95c

E = 140.06*3.20 MeV = 448.19 MeV

Now

= 425.74 Mev/c

3c.

Conservation of energy and momentum gives:

= rest mass energy of pion = 140.06 MeV

and

Since pion is at rest,

hence,

Since total energy of neutrino =

Then total mass of muon =

where rest mass of muon = 106 MeV

then

4d. total energy of muon =

solving this, we will get v = 0.86 c

velocity of muon = 0.86c = 2.60*108 m/sec.