In a hydrogen atom,an electron transitions from an orbit of radius $R$ to an orbit of radius $4R$. What is the ratio of their time periods?

The following statements are given about the hydrogen atom:
$A$. The wavelengths of the spectral lines of the Lyman series are greater than the wavelength of the second spectral line of the Balmer series.
$B$. The orbits correspond to circular standing waves in which the circumference of the orbit equals a whole number of wavelengths.

In hydrogen atoms, the radius of the smallest orbit of the electron is $a_0$. The radius of the third orbit is:

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?

The concept of stationary orbits was proposed by

In a system, a particle $A$ of mass $m$ and charge $-2q$ is moving in the nearest orbit around a very heavy particle $B$ having charge $+q$. Assuming Bohr's model of the atom to be applicable to this system, the orbital angular velocity of the particle $A$ is