Integrated Concepts

Particles called muons exist in cosmic rays and can be created in particle accelerators. Muons are very similar to electrons, having the same charge and spin, but they have a mass 207 times greater. When muons are captured by an atom, they orbit just like an electron but with a smaller radius, since the mass in $a_{\text{B}} = \frac{h^{2}}{4π^{2} m_{e} \text{kq}_{e}^{2}} = \text{0}.\text{529} \times \text{10}^{- \text{10}} \text{ m}$ is 207 $m_{e}$.

(a) Calculate the radius of the $n = 1$ orbit for a muon in a uranium ion ($Z = \text{92}$).

(b) Compare this with the 7.5-fm radius of a uranium nucleus. Note that since the muon orbits inside the electron, it falls into a hydrogen-like orbit. Since your answer is less than the radius of the nucleus, you can see that the photons emitted as the muon falls into its lowest orbit can give information about the nucleus.