If an electron is moving in the $n^{\text{th}}$ orbit of the hydrogen atom,then its velocity $(v_n)$ for the $n^{\text{th}}$ orbit is given as:

$A$ particle of mass $m$ moves in a circular orbit in a central potential field $U(r) = U_{0}r^{4}$. If Bohr's quantization conditions are applied,the radii of possible orbitals $r_{n}$ vary with $n^{1/\alpha}$,where $\alpha$ is ....... .

The ground state energy of a hydrogen atom is $-13.6 \; eV$. What are the kinetic and potential energies of the electron in this state?

Assertion $(A)$: The magnetic moment $(\mu)$ of an electron revolving around the nucleus decreases with increasing principal quantum number $(n)$.
Reason $(R)$: Magnetic moment of the revolving electron,$\mu \propto n$.

In Bohr's model of the hydrogen atom,the ratio between the period of revolution of an electron in the orbit of $n=1$ to the period of revolution of the electron in the orbit $n=2$ is

Energy levels $A, B, C$ of a certain atom correspond to increasing values of energy,i.e.,$E_A < E_B < E_C$. If $\lambda_1, \lambda_2, \lambda_3$ are the wavelengths of radiations corresponding to the transitions $C$ to $B$,$B$ to $A$,and $C$ to $A$ respectively,which of the following statements is correct?