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:

$A$ hydrogen ion $(H^+)$ and a singly ionized helium atom $(He^+)$ are accelerated from rest through the same potential difference $(V)$. The ratio of the final speeds of the hydrogen ion and the helium ion is close to:

Obtain an expression for the frequency of radiation emitted when a hydrogen atom de-excites from level $n$ to level $(n-1)$. For large $n$,show that this frequency equals the classical frequency of revolution of the electron in the orbit.

Which state of triply ionised Beryllium $(Be^{+++})$ has the same orbital radius as that of the ground state of hydrogen?

The energy of an electron in the ground state of a hydrogen atom is $E$. What is the energy of an electron in the $2^{nd}$ excited state of $Li^{++}$?

$A$ monochromatic radiation of wavelength $\lambda$ is incident on a hydrogen sample in ground state. The sample subsequently emits radiation of six different wavelengths, then the value of $\lambda$ is. [Use $hc = 1242 \text{ eV-nm}$] (in $\text{ nm}$)