Muon ( μ⁻) is a negatively charged (|q| = |e|) particle with a mass m… | JEE Main 2018 (15 Apr, Shift 2)

Q106JEE Main 2018 · 15 APR · SHIFT 2Medium

Bohr Model: Orbits, Speed & Angular Momentum

Muon ( $\mu^-$ ) is a negatively charged (|q| = |e|) particle with a mass m $\mu$ = 200 me, where me is the mass of the electron and e is the electronic charge. If $\mu^-$ 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 $\mu^-$ in the nth orbit is $\frac{1}{200}$ times that of the electron in the nth orbit. (C) The ionization energy of muonic atom is 200 times more than that of a hydrogen atom. (D) The momentum of the muon in the nth orbit is 200 times more than that of the electron.

Show answer and solution

Answer: (b)

(A) $r = \frac{\epsilon_0 n^2 h^2}{\pi m e^2} \propto \frac{1}{m}$ : 200 times smaller. True.
(B) $v = \frac{e^2}{2\epsilon_0 n h}$ does not depend on $m$ : same speed. False.
(C) $E = \frac{me^4}{8\epsilon_0^2 h^2} \propto m$ : 200 times more. True.
(D) $p = mv$ with the same $v$ : 200 times more. True.
So the answer is (b) (A), (C), (D).

Report a mistake

Bohr Model: Orbits, Speed & Angular Momentum question from JEE Main 2018 (15 Apr, Shift 2)

More questions on Bohr Model: Orbits, Speed & Angular Momentum