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 $: 1$)?

An ionic atom equivalent to a hydrogen atom has a wavelength equal to $1/4$ of the wavelength of the corresponding hydrogen line. The ion is:

$A$ small particle of mass $m$ moves in such a way that its potential energy $U = \frac{1}{2} m \omega^2 r^2$,where $\omega$ is a constant and $r$ is the distance of the particle from the origin. Assuming Bohr's quantization of angular momentum and a circular orbit,the radius of the $n^{\text{th}}$ orbit will be proportional to:

Write the theoretical value and experimental value of the Rydberg constant,including the unit.

If one were to apply the Bohr model to a particle of mass $m$ and charge $q$ moving in a plane under the influence of a magnetic field $B$,the energy of the charged particle in the $n^{th}$ level will be

The magnitude of acceleration of the electron in the $n$th orbit of a hydrogen atom is $a_{H}$ and that of a singly ionised helium atom is $a_{He}$. The ratio of $a_{H} : a_{He}$ is