# Hydrogen atom, muon substitution

1. Sep 13, 2010

### rayman123

1. The problem statement, all variables and given/known data
Substitute an electron in a neutral hydrogen atom with a muon.
a) calculate the Bohr radius of the ground state for this myonic atom of atom. The answer must be right to at least 2 significant digits.
b) Calculate the fraction of the myon that is located inside the proton, which can be assumed to have radius of 1.3fm.
c) Helium can not form negative ions with electrons, although hydrogen can. Is it possible to form negatively charged helium atom if you try attach a myon to the atom?

2. Relevant equations

a) $$r_{n} = \frac{\epsilon_{0} \cdot h^2\cdot n^2}{\pi\cdot \mu \cdot e^2\cdot Z}= 2.56034\cdot 10^{-13}m$$

$$r_{p}= 1.3\cdot 10^{-15}$$

b) not sure if I that is correct how to calculate that fraction....
$$\frac{2.56043\cdot 10^{-13}}{1.3\cdot 10^{-15}}= 196.9492$$
now the fraction of the muon which is located in the proton will be

$$196.9492 \cdot 2.56043\cdot 10^{-13}= 5.04275\cdot10^{-11}$$ ???? is that correct?

c) I have just found some publications where actually such atoms have been formed, where muons where stuck to helium atoms forming negative charged atoms.

Thanks

Last edited: Sep 13, 2010