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

If the electronic charge on an electron alone is doubled, then as per the Bohr model, the $K.E.$ of an $e^-$ revolving in the $n^{th}$ orbit becomes:

If $m$ is the mass of an electron,$v$ is its velocity,$r$ is the radius of a stationary circular orbit around a nucleus with charge $Ze$,then from Bohr's first postulate,the kinetic energy of the electron is (where $K = 1 / 4 \pi \epsilon_0$):

An electron in a hydrogen atom makes a transition from $n_1$ to $n_2$. If the time period of the electron in the initial state is eight times that in the final state,then:

The ionization potential for the second $He$ electron is ...... $eV$.

$A$ small particle of mass $m$ moves in such a way that its potential energy $U = \frac{1}{2} m \omega^2 r^2$,where $\omega$ is a constant and $r$ is the distance of the particle from the origin. Assuming Bohr's quantization of angular momentum and a circular orbit,the radius of the $n^{\text{th}}$ orbit will be proportional to: