If the ionization energy of a hydrogen atom is $E$,then the ionization energy of $Li^{2+}$ will be ............ $E$.

The energy of a photon of wavelength $(\lambda) = 1 \, m$ is (Planck's constant $= 6.626 \times 10^{-34} \, J \, s$,speed of light $= 3 \times 10^8 \, ms^{-1}$)

The work function of a metal $M$ is $6.3 \ eV$. The wavelength of the incident radiation required to just eject the electrons from its surface (in $nm$) is

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.

The energy of the first (lowest) Balmer line of the $H$ atom is $x \ J$. The energy (in $J$) of the second Balmer line of the $H$ atom is:

The potential energy of an electron in the hydrogen atom is $-6.8 \ eV$. Indicate in which excited state the electron is present.