Question

2. Fine structure constant α, for electrons defined as

α≡v/c

where v is the speed of electrons around the atomic nucleus and c is the speed of light. The negative Muon particle (μ^-) is a subatomic particle that has the type and magnitude of the charge equal to an electron, but has a mass 207 times the mass of the electron. These negative muons can be attracted by protons and form hydrogen-like structures called muonic hydrogen atoms. Determine:

a. The velocity of muons around the proton!

b. Fine structure constants for muon in muonic hydrogen atom!

Course: Particle Physics

Answer 1

a) The velocity betweeb muons around the proton is given,for n= 1 state:

where,

In other word,

and   

Since the charge of muon is -1e = 1.6*10^-19C

*** The velocity is independent of the mass of the revolving particle.

b) The fine structure of muon is given by the same relation as that of electron. It is a dimensionless quantity and doesnot depend on the mass.

,