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

$A$ beam of monochromatic light is used to excite the electron in $Li^{++}$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x \times 10^{-10} \; m$. The value of $x$ is $\dots$. [Given $hc = 1242 \; eV \cdot nm$]

Obtain the equations for the frequency of radiation and the wave number when an electron makes a transition from a higher energy state to a lower energy state in a hydrogen atom.

The ratio of the time periods of the revolution of the electrons in the second and third excited states 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:

The de Broglie wavelength of an electron revolving in the first Bohr orbit of circumference $2\pi r$ is ............