Muon (μ⁻) is a negatively charged (|q|=|e|) particle with a mass m_μ=200mₑ, where mₑ is the mass of the electron and e is the electronic charge. If μ⁻ is bound to a proton to form a hydrogen like atom, identify the correct statements. (A) Radius of the muonic orbit is 200 times smaller than that of…

Question

Muon (μ⁻) is a negatively charged (|q|=|e|) particle with a mass m_μ=200mₑ, where mₑ is the mass of the electron and e is the electronic charge. If μ⁻ is bound to a proton to form a hydrogen like atom, identify the correct statements.
(A) Radius of the muonic orbit is 200 times smaller than that of the electron.
(B) The speed of the μ⁻ in the n^th orbit is 1/(200) times that of the electron in the n^th orbit.
(C) The ionization energy of muonic atom is 200 times more than that of an hydrogen atom.
(D) The momentum of the muon in the nth orbit is 200 times more than that of the electron.

Accepted Answer

(3) A, C, D. r∝1/m: 200 times smaller (A true). v=(e²)/(2ε₀nh) has no mass: same speed (B false). E∝ m: 200 times (C true). p=mv: 200 times (D true).

Step-by-step solution

Why the other options are wrong