Ratio of centripetal acceleration for an electron revolving in $3^{\text{rd}}$ orbit and $5^{\text{th}}$ Bohr orbit of hydrogen atom is

In the Bohr's hydrogen atom model,the radius of the stationary orbit is directly proportional to ($n =$ principle quantum number)

Assuming the atom is in the ground state,the expression for the magnetic field at the nucleus in a hydrogen atom due to the circular motion of the electron is: $[\mu_0 \rightarrow \text{permeability of free space, } m \rightarrow \text{mass of electron, } \varepsilon_0 \rightarrow \text{permittivity of free space, } h \rightarrow \text{Planck's constant}]$

If the energy of the $n^{th}$ orbit in a hydrogen atom is $E_n$,what will be the energy of the $n^{th}$ orbit in a helium ion $(He^+)$?

The number of absorption transitions between the first and the fourth energy states of a hydrogen atom is $3$. The number of emission transitions between these states will be

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 $Å$)