QJEEM18Ph1325: JEE Main 2018 Physics - Class 12 JEEM18Ph1325 Solution: Muon ( μ − ) is a negatively charged (

(i) Radius of the orbit is given by

$$r=\frac{h^2}{4\pi m{e}^2}\times \frac{n^2}{Z}$$

Only, m_$$\mu$$ = 200 m_e rest are same. So, statement (A) is correct: The radius of muonic orbit is 200 times smaller than that of the electron.

(ii) Velocity of particle in an orbit is given by

$$v=\frac{nh}{2\pi mr}=\frac{nh\times 4\pi m{e}^2\times Z}{2\pi m\times h^2\times n^2}=\frac{2e^{2}Z}{hn}$$

Therefore, speed does not change as it does not depend on mass. So, statement (B) is incorrect.

(iii) Ionisation energy is given by

$$\mathrm{\Delta }{E}_n=-\frac{2{\pi }^{2}m{e}^4{Z}^2}{h^2{(4\pi {\epsilon }_0)}^2}\times \left(\frac{1}{n_2^2}-\frac{1}{n_1^2}\right)$$

Only, m_$$\mu$$ = 200 m_e rest are same. So, statement (C) is correct: The ionisation energy of muonic atom is 200 times more than that of an hydrogen atom.

(iv) Since Momentum $$\propto$$ Energy. So, statement (D) is correct: The momentum of the muon in he nth orbit is 200 times more than that of the electron.