In Bohr's model of the hydrogen atom,the ratio between the period of revolution of an electron in the orbit of $n=1$ to the period of revolution of the electron in the orbit $n=2$ is

Consider an electron in the $n=3$ orbit of a hydrogen-like atom with atomic number $Z$. At absolute temperature $T$,a neutron having thermal energy $k_B T$ has the same de Broglie wavelength as that of this electron. If this temperature is given by $T = \frac{Z^2 h^2}{\alpha \pi^2 a_0^2 m_N k_B}$,(where $h$ is the Planck's constant,$k_B$ is the Boltzmann constant,$m_N$ is the mass of the neutron and $a_0$ is the first Bohr radius of hydrogen atom),then the value of $\alpha$ is $....$

If a proton had a radius $R$ and the charge was uniformly distributed,calculate using Bohr theory,the ground state energy of a $H$-atom when $(i) R = 0.1 \mathring{A}$ and $(ii) R = 10 \mathring{A}$.

The frequency of revolution of an electron in the $n^{\text{th}}$ orbit of a hydrogen atom is

According to Bohr's theory,the moment of momentum of an electron revolving in the $4^{\text{th}}$ orbit of a hydrogen atom is:

What is the ratio of the time periods of an electron in the $n = 2$ and $n = 1$ orbits of a hydrogen atom (in $:1$)?