The radius of the innermost orbit of a hydrogen atom is $5.3 \times 10^{-11} \ m$. The radius of the fourth allowed orbit of the hydrogen atom is: (in $Å$)

The wavelength of the energy emitted when an electron transitions from the fourth orbit to the second orbit in a hydrogen atom is $20.397 \, cm$. The wavelength of the energy for the same transition in $He^+$ is .......... $cm$.

Find the radius of $Be^{3+}$ ions in its ground state assuming Bohr's model to be valid $(a_0 = 53 \ pm)$. (in $pm$)

Hydrogen $(H)$,deuterium $(D)$,singly ionized helium $(He^+)$ and doubly ionized lithium $(Li^{2+})$ all have one electron around the nucleus. Consider the $n = 2$ to $n = 1$ transition. The wavelengths of emitted radiations are $\lambda_1, \lambda_2, \lambda_3$ and $\lambda_4$ respectively. Then approximately:

The Bohr model of atoms:

$A$ 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 $eV$)