The energy required to excite an electron in a hydrogen atom from the ground state $(n=1)$ to the first excited state $(n=2)$ is $..........$ $eV$.

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.

If the shortest wavelength of the Lyman series of the $H$ atom is $x$,then calculate the total energy of the $H$ atom in the first excited state.

The radius of a hydrogen atom in its ground state is $0.53 \ \mathring{A}$. The radius of the $Li^{2+}$ ion in the same state (atomic number = $3$) is ............. $\mathring{A}$.

If the first ionization energy of $H$ atom is $13.6 \ eV,$ then the second ionization energy of $He$ atom is (in $eV$)

The energy of an electron in the first Bohr orbit of the hydrogen atom is $-13.6 \ eV$. Calculate the energy of an electron in the first Bohr orbit of $He^{+}$ in $eV$.