The radius of the innermost electron orbit of a hydrogen atom is $5.3 \times 10^{-11} \ m$. What is the ratio of the radii of the orbits for $n=2$ and $n=3$?

How is the linear velocity $v$ of an electron in a $Bohr$ orbit related to its principal quantum number $n$?

If the energy required to remove one of the two electrons from a $He$ atom is $29.5 \,eV$,then what is the total energy required to convert a helium atom into an $\alpha$-particle (i.e.,$He^{2+}$ ion)?

$A$ hydrogen-like atom has one electron revolving around a stationary nucleus. If the energy required to excite the electron from the $2^{nd}$ orbit to the $3^{rd}$ orbit is $47.2 \ eV$,find the atomic number of the given atom.

The de-Broglie wavelength of an electron in the $3^{rd}$ orbit of a $He^{+1}$ ion is approximately (in $\mathring{A}$):

In a hydrogen atom,when an electron transitions from the $4^{th}$ orbit to the $2^{nd}$ orbit,the wave number is $20,397 \, cm^{-1}$. What will be the wave number when an electron in a $He^+$ ion transitions from the $4^{th}$ orbit to the $2^{nd}$ orbit?