The most probable radius (in $pm$) for finding the electron in $He^{+}$ is

In the hydrogen spectrum,the energy during the first Lyman transition is $E = 10.2 \ eV$. The same energy is observed during the second Balmer series transition in which of the following species?

The kinetic energy of electrons emitted, when radiation of frequency $1.0 \times 10^{15} \ Hz$ hits a metal, is $2 \times 10^{-19} \ J$. What is the threshold frequency of the metal (in $Hz$)?
$(h = 6.6 \times 10^{-34} \ Js)$

The light of wavelength $242 \, nm$ is required to remove an electron from a $Na$ atom. What is the ionization energy of the sodium atom in $kJ \, mol^{-1}$?

When a certain metal was irradiated with light of frequency $4.0 \times 10^{16} \ s^{-1}$,the photoelectrons emitted had four times the kinetic energy as the kinetic energy of photoelectrons emitted when the same metal was irradiated with light of frequency $2.0 \times 10^{16} \ s^{-1}$. The threshold frequency $(v_0)$ of the metal in $s^{-1}$ is

Explain the following according to Bohr's model of hydrogen:
$(i)$ Principal quantum number
$(ii)$ Radius of stationary orbit $(r)$
$(iii)$ Energy of stationary state
$(iv)$ Isoelectronic ion of $H$
$(v)$ Velocity of electron