A muon is an unstable elementary particle whose mass is 207 m e and whose charge is either +e or – e. A negative muon (µ – ) can be captured by a nucleus to form a muonic atom. Suppose a proton captures a negative muon (µ – ), find the radius of first Bohr orbit and the ionization energy of the atom. (Take mass of proton m p = 1836 m e , where m e is mass of electron).
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Reduced mass of a system of two particles is given by
µ = 
= 
= 186 m e ,
Radius corresponding to the reduced mass µ is given by
r′ 1 = 
r 1 = 
a 0 = 2.85 × 10 –13 m
Where a 0 is the radius of first Bohr orbit of ordinary hydrogen atom. a 0 = 5.29 × 10 –11 m.
Ionization energy is given by E′ 1 = 
E 1 = 186 E 1 = – 2.53 × 10 3 eV. Where E 1 is the ionization energy of ordinary hydrogen atom.
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