An electron in an atom jumps in such a way that its kinetic energy changes from $x$ to $\frac{x}{4}$. The change in potential energy will be

The ratio of the lowest energy in terms of wave numbers of the Balmer and Lyman series of lines of the atomic spectrum of hydrogen is

Light of frequency $1.6 \times 10^{16} \ Hz$ falling on a metal plate emits electrons that have double the kinetic energy compared to the kinetic energy of electrons emitted when light of frequency $1.0 \times 10^{16} \ Hz$ falls on the same plate. The threshold frequency $(v_0)$ of the metal in $Hz$ is:

The radius ratio of Bohr's first orbit of hydrogen-like species $He^{+}$,$Li^{2+}$,and $Be^{3+}$ is:

For the $H$ atom,which of the following is the correct order of energy?

In the atomic spectrum of hydrogen, the wavelengths of the spectral lines corresponding to electronic transitions $(i)$ $n=4$ to $n=2$ and $(ii)$ $n=3$ to $n=1$ are $\lambda_1$ and $\lambda_2$ $\mathring{A}$ respectively. The value of $(\lambda_1-\lambda_2)$ (in cm) is ($R_H$ = Rydberg constant)