The radius of the first permitted Bohr orbit for the electron, in a hydrogen atom equals 0.51 Å and its ground state energy equals -13.6 eV . If the electron in the hydrogen atom is replaced by muon ( ⁻¹ ) [Charge same as electron and mass 207 ~m _ e ], the first Bohr radius and ground state energy will be

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Key Idea Hydrogen atom can be considered to be the system of two charges, positive charged nucleus and negative charged electron. A system of this kind is equivalent to a single particle of mass m^ that revolves around the position of the heavier particle. Then, the reduced mass of electron is m^ = m M m+M where, m= mass of electron and M= mass of nucleus Its values is less than m . Given, radius of first orbit for electron r ₁=0.51 Å , ground state energy of electron, E ₁=-13.6 eV , mass of electron = m _ e mass o