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 ............. $\mathring{A}$.

An electronic transition in a hydrogen atom results in the formation of the $H_\alpha$ line of the hydrogen spectrum in the Lyman series. The energies associated with the electron in each of the orbits involved in the transition (in $kcal \ mol^{-1}$) are:

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 $kJ \, mol^{-1}$?

If in a hydrogen atom,an electron jumps from the $3^{rd}$ Lyman line to the $1^{st}$ Lyman line,then the obtained wavelength is:

When electromagnetic radiation of wavelength $310 \ nm$ falls on the surface of a metal having work function $3.55 \ eV$, the velocity of photoelectrons emitted is $x \times 10^5 \ ms^{-1}$. The value of $x$ is (Nearest integer). Given: $m_{e} = 9 \times 10^{-31} \ kg$, $h = 6.63 \times 10^{-34} \ J \cdot s$, $c = 3 \times 10^8 \ m/s$, $1 \ eV = 1.6 \times 10^{-19} \ J$.

The photoelectric behaviour of $K$,$Li$,$Mg$,and $Ag$ metals is shown in the plot below. If light of wavelength $400 \ nm$ is incident on each of these metals,which of them will emit photoelectrons?
[Planck's constant $h=6.626 \times 10^{-34} \ J \ s$; velocity of light $c=3 \times 10^8 \ m \ s^{-1}$; $1 \ eV = 1.6 \times 10^{-19} \ J$]