Question

A muon of charge $-e$ and mass $m=207 m_{e}$ (where $m_{e}$ is the mass of an electron) orbits the nucleus of a singly ionized helium atom (He $^{+}$ ). Assuming that the Bohr model of the hydrogen atom can be applied to this muon-helium system, verify that the energy levels of the system are given by $$E=-\frac{11.3 \mathrm{keV}}{n^{2}}$$

          A muon of charge $-e$ and mass $m=207 m_{e}$ (where $m_{e}$ is the mass of an electron) orbits the nucleus of a singly ionized helium atom (He $^{+}$ ). Assuming that the Bohr model of the hydrogen atom can be applied to this muon-helium system, verify that the energy levels of the system are given by 
$$E=-\frac{11.3 \mathrm{keV}}{n^{2}}$$

Added by Noelia M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

05/29/2023

Step 1

The energy levels of a hydrogen-like atom are given by the formula: $$E = -\frac{Z^2 e^4 m}{8 \epsilon_0^2 h^2 n^2}$$ where $Z$ is the atomic number, $e$ is the elementary charge, $m$ is the mass of the orbiting particle, $\epsilon_0$ is the vacuum permittivity, Show more…

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A muon of charge $-e$ and mass $m=207 m_{e}$ (where $m_{e}$ is the mass of an electron) orbits the nucleus of a singly ionized helium atom (He $^{+}$ ). Assuming that the Bohr model of the hydrogen atom can be applied to this muon-helium system, verify that the energy levels of the system are given by $$E=-\frac{11.3 \mathrm{keV}}{n^{2}}$$