By applying Bohr’s model to a muonic atom, which consists of a nucleus of charge with a negative muon (an elementary particle with a charge and a mass , where is the electron mass) circulating about it, we have to calculate (a) the muon-nucleus separation in the first Bohr orbit, (b) the ionization energy, and (c) the wavelength of the most energetic photon that can be emitted. We may assume that the muon is circulating about a hydrogen nucleus .

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We will take into account the finite mass of the nucleus by using the reduce mass for the mass of the orbiting muon, that is

(a)

The muon-nucleus separation in the first Bohr orbit will be given by

We have used that the Bohr radius

(b)

The ionization energy of the muonic atom will be

(c)

The wavelength of the most energetic photon that can be emitted by a muonic atom will be