The energy of an electron in an excited hydrogen atom is $-3.4\mathrm{eV}$. Calculate the angular momentum of the electron according to Bohr's theory. Given : Rydberg's constant  $\mathrm{R}=1.09737\times {10}^{-7}{ \mathrm{m}}^{-1}$, Planck's constant $\mathrm{h}=6.626176\times {10}^{-34} \mathrm{Js}$, speed of light $e=3\times {10}^8 \mathrm{m}/\mathrm{s}$

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

A particle of charge equal to that of an electron $-\mathrm{e}$ and mass $208$ times the mass of an electron (called mu -meson) moves in a circular orbit around a nucleus of charge $+3\mathrm{e}$ (Take the mass of nucleus to be infinite). Assuming that the Bohr model is applicable to this system. Find the value of $\mathrm{n}$ for which the radius of the orbit is approximately the same as that of the first Bohr orbit for the hydrogen atom.

A particle of charge equal to that of an electron $-\mathrm{e}$ and mass $208$ times the mass of an electron (called mu -meson) moves in a circular orbit around a nucleus of charge $+3\mathrm{e}$ (Take the mass of nucleus to be infinite). Assuming that the Bohr model is applicable to this system, Find the wavelength of the radiation emitted when the mu-meson jumps from the third orbit to the first orbit.

A hydrogen-like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transitions between a group of levels. These levels have energies $-0.85\mathrm{eV}$ and $-0.544\mathrm{eV}$ (including both these values) 

Find the atomic number of the atom.

A hydrogen-like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transitions between a group of levels. These levels have energies $-0.85\mathrm{eV}$ and $-0.544\mathrm{eV}$ (including both these values) 

Calculate the smallest wavelength emitted in these transitions. (Take $\mathrm{hc}=1240\mathrm{eVnm}$, ground state of hydrogen atom $=-13.6\mathrm{eV}$)