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 electron in a hydrogen atom makes a transition $n_1 \rightarrow n_2$,where $n_1$ and $n_2$ are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The frequency of orbital motion of the electron in the initial state is $1/27$ of that in the final state. The possible values of $n_1$ and $n_2$ are

A hydrogen atom, initially in the ground state, is excited by absorbing a photon of wavelength $980 \ \text{\AA}$. The radius of the atom in the excited state, in terms of Bohr radius $a_0$, will be (given $hc = 12500 \ \text{eV-\AA}$). (in $a_0$)

The magnetic moment $(\mu)$ of an electron revolving around the nucleus varies with the principal quantum number $n$ as

In a hydrogen atom,let $R$,$v$,and $E$ denote the radius,velocity,and total energy of the electron,respectively. Then,the principal quantum number $n$ is proportional to which of the following?

The figure shows standing de-Broglie waves due to the revolution of an electron in a certain orbit of a hydrogen atom. Then,the expression for the orbit radius is (All notations have their usual meanings).