The figure shows a graph between $\ln \left| \frac{A_n}{A_1} \right|$ and $\ln |n|$, where $A_n$ is the area enclosed by the $n^{th}$ orbit in a hydrogen-like atom. The correct curve is

What is the minimum energy that must be given to a $H$ atom in the ground state so that it can emit an $H_{\gamma}$ line in the Balmer series? If the angular momentum of the system is conserved,what would be the angular momentum of such an $H_{\gamma}$ photon?

An excited hydrogen atom emits a photon of wavelength $\lambda$ in returning to the ground state. The quantum number $n$ of the excited state is ($R=$ Rydberg's constant).

For $He^{+}$, a transition takes place from the orbit of radius $105.8 \ pm$ to the orbit of radius $26.45 \ pm$. The wavelength (in $nm$) of the emitted photon during the transition is. . . . .
[Use: Bohr radius, $a_0=52.9 \ pm$; Rydberg constant, $R_H=2.2 \times 10^{-18} \ J$; Planck's constant, $h=6.6 \times 10^{-34} \ J \ s$; Speed of light, $c=3 \times 10^8 \ m \ s^{-1}$]

The $21\, cm$ radio wave emitted by hydrogen in interstellar space is due to the interaction called the hyperfine interaction in atomic hydrogen. The energy of the emitted wave is nearly

Consider a hydrogen atom with its electron in the $n^{\text{th}}$ orbital. An electromagnetic radiation of wavelength $90 \ nm$ is used to ionize the atom. If the kinetic energy of the ejected electron is $10.4 \ eV$,then the value of $n$ is $(hc = 1242 \ eV \ nm)$.