Question

In the Bohr model of the hydrogen atom, the allowed orbits of the electron (labeled n = 1, 2, 3, …) have angular momentum , orbital radii , and energies . In these expressions me is the mass of the electron.

In an exotic atom the electron is replaced by a different subatomic particle that has the same charge as an electron but a different mass. Two examples that have been studied are muonic hydrogen, in which the electron is replaced by a muon of mass , and kaonic hydrogen, in which the electron is replaced by a kaon of mass . Mu = 207 Me, Mk = 966 Me

(a) Rank the radii of the lowest-energy orbits in (i) ordinary hydrogen, (ii) muonic hydrogen, and (iii) kaonic hydrogen, from largest radius to smallest radius. If any two of these orbits have the same radius, state this. Explain how you made your ranking.

(d) Rank the speeds of the particles orbiting the nucleus in the lowest-energy orbit of (i) ordinary hydrogen, (ii) muonic hydrogen, and (iii) kaonic hydrogen, from fastest to slowest. If the speed is the same in any two of these situations, state this. Explain how you made your ranking.

Answer 1

icolo al Radius Im Ze2 m nth orbit is given by nh งn In H-atom, m me In muoni alom, m mu = 207 me In kaonic atom, m m =966 me k ru sre H larges? vachios - Hydrsogon a bom lowest radius - kaonic alom velocity of ê in nth orbite is b) e2 h anho 1.e. velocity of é is indenfendent of mass of nutleus . All the atom have some velocity V H. vu - k