For a $H$-atom,what is the wavelength in $nm$ associated with the transition of an electron from an infinite energy level to the first energy level? (Rydberg constant = $1.097 \times 10^{7} \ m^{-1}$)

Threshold frequency,$v_0$ is the minimum frequency which a photon must possess to eject an electron from a metal. It is different for different metals. When a photon of frequency $1.0 \times 10^{15} \ s^{-1}$ was allowed to hit a metal surface,an electron having $1.988 \times 10^{-19} \ J$ of kinetic energy was emitted. Calculate the threshold frequency of this metal. Show that an electron will not be emitted if a photon with a wavelength equal to $600 \ nm$ hits the metal surface.

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 maximum energy is possessed by an electron when it is present:

According to Bohr's atomic theory :-
$A$. Kinetic energy of electron is $\propto \frac{Z^{2}}{n^{2}}$.
$B$. The product of velocity $(v)$ of electron and principal quantum number $(n)$,'$vn$' $\propto Z^{2}$.
$C$. Frequency of revolution of electron in an orbit is $\propto \frac{Z^{3}}{n^{3}}$.
$D$. Coulombic force of attraction on the electron is $\propto \frac{Z^{3}}{n^{4}}$.
Choose the most appropriate answer from the options given below :

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