# Homework Help: Muonic Atom

1. Feb 28, 2005

### PhatPartie

The electron in the Hydrogen atom can be replaced by the heavier muon resulting in a muonic atom. The muonic atom is not stable because the muon lives for 2.2 ms on average and then it decays into an electron and two neutrinos. However some very fast experiments can be performed on the muonic atom.

What is the energy of the muon in the ground state?

What is the radius of the muon's orbit in the ground state?

What is the speed of the muon in terms of the speed of the light when the muon is in the ground state?

- electron : 0.5110 Mev/c2,
- muon : 105.7 Mev/c2,
- proton : 938.3 Mev/c2.

A) so i tired E= -(alpha/2) *mc where m = Mmuon*Mproton/Mmuon+Mproton ...ended up getting an answer of -7.59 * 10^5 eV .... dont know what i did wrong?

2. Feb 28, 2005

### stunner5000pt

the energy is given by

$$E = -R_{M} \frac{hc}{n^2}$$

where Rm is the rydberg constant for that atom and is given by $$R_{M} = \frac{\mu}{m}R_{\infty}$$ R infinity is a constant that you can look up.
And $$\mu = \frac{mM}{m+M}$$

radius of the orbit is given by
$$r_{n} = \frac{n^2}{Z_{O} Z_{N}} \frac{\epsilon_{0} h^2}{\pi \mu e^2}$$
and Zo and Zn are the charges(in terms of integer multiple of e) of the orbiting particle and the nucleus respectively.

velocity is $$v_{n} = \frac{Z_{O} Z_{N}}{n} (7.3 * 10^{-3})$$