What is the ratio of the time period of revolution of an electron in the second orbit of a hydrogen atom to that in the third orbit of a $He^{+}$ ion?

Find the radius of the fourth orbit of a hydrogen atom if its radius of the first orbit is $R \text{ pm}$.

For a $H$ atom,the energy transition from $n = 1$ to $n = 2$ is $10.2 \ eV$. What will be the energy for the same transition in $Be^{3+}$ ion?

Calculate the longest wavelength in the hydrogen emission spectrum of the Lyman series $\left(R_H = 109677 \ cm^{-1}\right)$.

The radius of a hydrogen atom in its ground state is $0.53 \ \mathring{A}$. The radius of the $Li^{2+}$ ion in the same state (atomic number = $3$) is ............. $\mathring{A}$.

$A$ metal having a work function of $4 \, eV$ is exposed to a photon of $\lambda = 1240 \, \mathring{A}$. If an accelerating potential of $7.6 \, V$ is applied,then the electron with maximum kinetic energy will have a speed equal to -