The number of de-Broglie wavelengths contained in the second Bohr orbit of a hydrogen atom is

The energy required to ionise a hydrogen-like ion in its ground state is $9$ Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state to the ground state? ........$nm$

When an electron in a Hydrogen atom revolves in a stationary orbit,it

The ratio of wavelengths for the transition of electrons from the $2^{nd}$ orbit to the $1^{st}$ orbit of Helium $(He^+)$ and Lithium $(Li^{++})$ is (Atomic number of Helium = $2$,Atomic number of Lithium = $3$).

$A$ particle of mass $m$ moves in a circular orbit in a central potential field $U(r) = \frac{1}{2}kr^2$. If Bohr's quantization conditions are applied,radii of possible orbits and energy levels vary with quantum number $n$ as

An electron from various excited states of a hydrogen atom emits radiation to return to the ground state. Let $\lambda_n$ and $\lambda_g$ be the de Broglie wavelength of the electron in the $n^{th}$ state and the ground state,respectively. Let $\Lambda_n$ be the wavelength of the emitted photon in the transition from the $n^{th}$ state to the ground state. For large $n$,which of the following relations holds true ($A, B$ are constants)?