If the potential energy of an electron in the second orbit of $He^+$ is $-27.2 \, eV$,then calculate the double value of the energy of the first excited state of a hydrogen atom in $eV$.

The Bohr orbit radius for the hydrogen atom $(n = 1)$ is approximately $0.530 \ \mathring{A}$. The radius for the first excited state $(n = 2)$ orbit is ........... $\mathring{A}$

State whether the following statements are true or false:
$(i)$ The $Bohr$ model cannot explain how atoms form molecules.
$(ii)$ The $Bohr$ model is accepted as the planetary model.
$(iii)$ Electrons in an atom do not absorb or emit energy while moving in a stationary orbit.
$(iv)$ The spectral lines of the $Brackett$ series are found in the ultraviolet region.

An electron revolves in an orbit around a stationary nucleus with atomic number $Z = 5$. The energy required to excite the electron from the $3^{rd}$ orbit to the $4^{th}$ orbit is .......... $eV$.

The threshold frequency of a metal is $10^{15} \ s^{-1}$. The ratio of maximum kinetic energies of the photoelectrons,when the metal is irradiated with radiations of frequencies $1.5 \times 10^{15} \ s^{-1}$ and $2.0 \times 10^{15} \ s^{-1}$ respectively,is

$A$: An electron revolving around the nucleus does not fall into the nucleus.
$R$: An electron revolving around the nucleus is an orbital electron.