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:

$A$ particle of mass $m$ is moving around the origin with a constant force $F$ pulling it towards the origin. If Bohr model is used to describe its motion,the radius $r$ of the $n^{\text{th}}$ orbit and the particle's speed $v$ in the orbit depend on $n$ as

The angular momentum for the electron in the first Bohr orbit is $L$. If the electron is assumed to revolve in the second orbit of a hydrogen atom,then the change in angular momentum will be:

$A$ 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 $hc = 1242 \; eV \cdot nm$]

The ratio of the area of the first excited state to the ground state orbit of a hydrogen atom is:

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