If the radius of the first orbit of an $H$ atom is $a_0$, then the de Broglie wavelength of an electron in the third orbit is: (in $\pi a_0$)

De-Broglie wavelength of an electron orbiting in the $n=2$ state of a hydrogen atom is close to (Given Bohr radius $= 0.052 \ nm$) (in $nm$)

$A$ particular hydrogen-like ion emits radiation of frequency $3 \times 10^{15} \,Hz$ when it makes a transition from $n=2$ to $n=1$. The frequency of radiation emitted in a transition from $n=3$ to $n=1$ is $\frac{x}{9} \times 10^{15} \,Hz$, where $X = \text{ . . . . . . }$.

The ratio of the ionization energy of a Bohr's hydrogen atom to that of a Bohr's hydrogen-like lithium atom is:

$A$ moving Hydrogen atom makes a head-on collision with a stationary Hydrogen atom. Before the collision,both atoms are in the ground state,and after the collision,they move together. The minimum kinetic energy of the moving Hydrogen atom,such that one of the atoms reaches the excitation state,is (in $eV$)

For an electron moving in the $n^{th}$ orbit of an $H$-atom,the angular velocity is proportional to: