A particle of charge equal to that of an electron, $ -e $, and mass $ 208 $ times the mass of electron (called $ \mu-\operatorname{meson} $ ) moves in a circular orbit around a nucleus of charge $ +3 \mathrm{e} $. (Take the mass of the nucleus to be infinite). Assuming that Bohr model of the atom is applicable to this system: Derive an expression for the radius of the $ \mathrm{n}^{\text {th }} $ Bohr orbit

Question

A particle of charge equal to that of an electron, $ -e $, and mass $ 208 $ times the mass of electron (called $ \mu-\operatorname{meson} $ ) moves in a circular orbit around a nucleus of charge $ +3 \mathrm{e} $. (Take the mass of the nucleus to be infinite). Assuming that Bohr model of the atom is applicable to this system: Derive an expression for the radius of the $ \mathrm{n}^{\text {th }} $ Bohr orbit, $ \frac{\varepsilon_{0} \mathrm{n}^{2} \mathrm{~h}^{2}}{208 \pi \mathrm{m}_{\mathrm{e}} \mathrm{e}^{2}} $, $ \frac{\varepsilon_{0} \mathrm{n}^{2} \mathrm{~h}^{2}}{3 \pi \mathrm{m}_{\mathrm{e}} \mathrm{e}^{2}} $, $ \frac{\varepsilon_{0} \mathrm{n}^{2} \mathrm{~h}^{2}}{624 \pi \mathrm{m}_{\mathrm{e}} \mathrm{e}^{2}} $, $ \frac{\varepsilon_{0} \mathrm{n}^{2} \mathrm{~h}^{2}}{64 \pi \mathrm{m}_{\mathrm{e}} \mathrm{e}^{2}} $

MARKS App · Accepted Answer

Electrostatic force will provide required centripetal force for circular motion in bohr orbit. r n = n 2 h 2 ϵ 0 π m e 2 Z Put Z = 3 ; m = 208 m e

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