If an electron is moving in the $4^{\text{th}}$ orbit of the hydrogen atom,then the angular momentum of the electron in $SI$ units is

In a hydrogen atom in its ground state,the first Bohr orbit has radius $r_1$. When the atom is raised to one of its excited states,the electron's orbital velocity becomes one-third of its initial value. The radius of that orbit is: (in $r_1$)

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?

In a hydrogen atom,find the magnetic field at the center in the ground state. Given that Bohr's radius is $r_{0} = 5 \times 10^{-11} \, m$ (in $T$).

When an electron orbiting in a hydrogen atom in its ground state jumps to a higher excited state, the de-Broglie wavelength associated with it

The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is