Suppose an electron in an atom experiences an attractive force towards the nucleus given by $F = k/r$,where $k$ is a constant and $r$ is the distance of the electron from the nucleus. Applying the Bohr model to this system,the radius of the $n^{th}$ orbit $r_n$ and the kinetic energy of the electron in that orbit $K_n$ are found. Which of the following relationships is correct?

In an atom,two electrons move around the nucleus in circular orbits of radii $R$ and $4R$. The ratio of the time taken by them to complete one revolution is

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.

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?

Write the theoretical value and experimental value of the Rydberg constant,including the unit.

The radius of the first Bohr orbit is $r$. What is the radius of the $2^{nd}$ Bohr orbit?