In Bohr's theory of the hydrogen atom,'$r$' is the radius of the orbit,'$V$' is the speed of the electron, and '$E$' is the total energy of the electron. Which of the following physical quantities is inversely proportional to the principal quantum number '$n$'?

An electron is revolving in a circular orbit of radius $r$ in a hydrogen atom. The angular momentum of the electron is $L$. The relation between the magnetic dipole moment $(m)$ associated with it,the gyromagnetic ratio $(R)$,and $L$ is:

$A$ particular hydrogen-like ion emits radiation of frequency $3 \times 10^{15} \,Hz$ when it makes a transition from $n=2$ to $n=1$. The frequency of radiation emitted in a transition from $n=3$ to $n=1$ is $\frac{x}{9} \times 10^{15} \,Hz$, where $X = \text{ . . . . . . }$.

In a hydrogen atom and a $Li^{2+}$ ion,the electron is in the second excited state. If $l_{H}$ and $l_{Li}$ are the angular momenta of the electrons and $E_H$ and $E_{Li}$ are their respective energies,then:

Suppose an electron is attracted towards the origin by a force $F = \frac{k}{r}$,where $k$ is a constant and $r$ is the distance of the electron from the origin. By applying the Bohr model to this system,the radius of the $n^{th}$ orbital of the electron is found to be $r_n$ and the kinetic energy of the electron is $K_n$. Then which of the following is true?

Ratio of centripetal acceleration for an electron revolving in $3^{\text{rd}}$ orbit and $5^{\text{th}}$ Bohr orbit of hydrogen atom is