The ratio of the centripetal accelerations of the electron in two successive orbits of hydrogen is $81: 16$. Due to a transition between these two states,the angular momentum of the electron changes by ($h$ - Planck's constant).

The electron in a hydrogen atom makes a transition $n_1 \rightarrow n_2$,where $n_1$ and $n_2$ are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The frequency of orbital motion of the electron in the initial state is $1/27$ of that in the final state. The possible values of $n_1$ and $n_2$ are

If an electron is revolving around the hydrogen nucleus at a distance of $0.1 \,nm$, what should be its speed?

Given below are two statements:
Statement $I$: In a hydrogen atom,the frequency of radiation emitted when an electron jumps from a lower energy orbit $(E_1)$ to a higher energy orbit $(E_2)$ is given as $hf = E_1 - E_2$.
Statement $II$: The jumping of an electron from a higher energy orbit $(E_2)$ to a lower energy orbit $(E_1)$ is associated with the frequency of radiation given as $f = (E_2 - E_1) / h$.
This condition is Bohr's frequency condition. In the light of the above statements,choose the correct answer from the options given below.

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

In the Bohr model of the hydrogen atom,the centripetal force is provided by the Coulomb attraction between the proton and the electron. If $r_0$ is the radius of the ground state orbit,$m$ is the mass,$e$ is the charge on the electron,and $\varepsilon_0$ is the permittivity of vacuum,the speed of the electron is: