What is the ratio of the area of the orbit of an electron in the first excited state to that in the ground state of a hydrogen atom (in $: 1$)?

In the first excited state of a hydrogen atom, the energy of its electron is $-3.4 \text{ eV}$. The radial distance of the electron from the hydrogen nucleus in this case is approximately: (Take $1 \text{ eV} = 1.6 \times 10^{-19} \text{ J}$, $e = 1.6 \times 10^{-19} \text{ C}$ and $\frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \text{ N m}^2/\text{C}^2$)

The frequency of the $1^{st}$ line of the Balmer series in the ${H_2}$ atom is ${\nu _0}$. What is the frequency of the corresponding line emitted by a singly ionized ${He^+}$ atom?

The radius of the fifth orbit of the $Li^{++}$ ion is $......... \times 10^{-12} \ m$. Take: radius of the hydrogen atom (first Bohr radius) $r_0 = 0.51 \ \mathring{A}$.

The radius of the first Bohr orbit is $r$. What is the radius of the $2^{nd}$ Bohr orbit?

When the electron orbiting in a hydrogen atom goes from one orbit to another orbit (principal quantum number $= n$),the de-Broglie wavelength $(\lambda)$ associated with it is related to $n$ as: