A hydrogen atom, initially in the ground state, is excited by absorbing a photon of wavelength $980 \ \text{\AA}$. The radius of the atom in the excited state, in terms of Bohr radius $a_0$, will be (given $hc = 12500 \ \text{eV-\AA}$). (in $a_0$)

$A$ hydrogen-like atom has one electron revolving around a stationary nucleus. If the energy required to excite the electron from the $2^{nd}$ orbit to the $3^{rd}$ orbit is $47.2 \ eV$,find the atomic number of the given atom.

According to Bohr's theory,the angular momentum of an electron revolving in the second orbit of a hydrogen atom will be:

The wavelength for an electron in an orbit of a hydrogen atom is $10^{-9} \ m$. The principal quantum number for this electron is:

In the Bohr model of a hydrogen atom,the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If ${a_0}$ is the radius of the ground state orbit,$m$ is the mass,$e$ is the charge on the electron,and ${\varepsilon _0}$ is the vacuum permittivity,the speed of the electron is:

Hydrogen $(H)$,deuterium $(D)$,singly ionized helium $(He^+)$ and doubly ionized lithium $(Li^{++})$ all have one electron around the nucleus. Consider the $n = 2$ to $n = 1$ transition. The wavelengths of emitted radiations are $\lambda_1, \lambda_2, \lambda_3$ and $\lambda_4$ respectively.