The value of the energy for the first excited state of hydrogen atom will be $............. \ eV$.

When $Z$ is doubled in an atom,which of the following statements are consistent with Bohr's theory?

$A$ photon of wavelength $4 \times 10^{-7} \, m$ strikes on a metal surface. The work function of the metal is $2.13 \, eV$. Calculate:
$(i)$ The energy of the photon in $eV$.
$(ii)$ The kinetic energy of the emission in $eV$.
$(iii)$ The velocity of the photoelectron in $ms^{-1}$ ($1 \, eV = 1.6020 \times 10^{-19} \, J$,mass of electron $m = 9.10939 \times 10^{-31} \, kg$).

Match List-$I$ with List-$II$.

List-$I$ (Spectral Series for Hydrogen)	List-$II$ (Spectral Region)
$A$. Lyman	$I$. Infrared region
$B$. Balmer	$II$. $UV$ region
$C$. Paschen	$III$. Infrared region
$D$. Pfund	$IV$. Visible region

Choose the correct answer from the options given below:

If $P.E.$ of $3^{rd}$ shell is $-20 \ eV/atom$,then find the $I.P.$ of the $3^{rd}$ shell of that element.

In Bohr's atomic model,the radius $(r)$ and energy $(E)$ of an orbit $(n)$ are related as: