A negatively charged muon ( ) has the same charge magnitude as the electron but a mass
CHEMISTRY · Multi-part · CBSE · Chemistry · Structure of Atom · Structure of Atom
Problem
A negatively charged muon (μ−) has the same charge magnitude as the electron but a mass mμ≈207me. When captured by a proton, it forms a muonic hydrogen atom in which the muon moves in a circular orbit about the proton.
(a) Derive a symbolic expression for the orbital radius of a muon in the lowest-energy circular orbit about a single proton, expressed in terms of the Bohr radius a0 and the mass ratio mμ/me. Clearly state each step in your derivation.
(b) Compute the numerical value of this muonic-hydrogen radius using a0=5.29×10−11m.
(c) Determine the muon’s orbital speed in this lowest-energy orbit.
(d) Calculate the centripetal acceleration experienced by the muon and compare it quantitatively with that of an electron in the ground-state orbit of ordinary hydrogen. Provide the ratio of the two accelerations.