The ratio of angular momentum of an electron in $n^{\text{th}}$ orbit of a hydrogen atom to the velocity of the electron in the $n^{\text{th}}$ orbit is proportional to

$(a)$ Using the Bohr model,calculate the speed of the electron in a hydrogen atom in the $n = 1, 2,$ and $3$ levels.
$(b)$ Calculate the orbital period in each of these levels.

In any Bohr orbit of the hydrogen atom,the ratio of kinetic energy to potential energy of the electron is

Which state of triply ionised beryllium $(Be^{3+})$ has the same orbital radius as that of the ground state of hydrogen?

If $m$ is the mass of an electron,$v$ is its velocity,$r$ is the radius of a stationary circular orbit around a nucleus with charge $Ze$,then from Bohr's first postulate,the kinetic energy of the electron is (where $K = 1 / 4 \pi \epsilon_0$):

$A$ muon is an unstable particle with a mass of $207 \, m_e$ and a charge of either $+e$ or $-e$. $A$ muon $(\mu^-)$ is captured by a hydrogen nucleus to form a muonic atom. If the proton captures the $\mu^-$, find the ionization energy of this atom in $keV$.