Using Bohr's model,calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{nd}$ and $4^{th}$ orbits of hydrogen atom. (in $32$ : $1$)

The difference between the radii of $n^{\text{th}}$ and $(n+1)^{\text{th}}$ orbits of a hydrogen atom is equal to the radius of the $(n-1)^{\text{th}}$ orbit of hydrogen. The angular momentum of the electron in the $n^{\text{th}}$ orbit is $.........$ ($h$ is Planck's constant).

The radius of the smallest electron orbit in a hydrogen-like ion is $(0.51/4 \times 10^{-10}) \text{ m}$. This ion is:

The radius of the innermost orbit of a hydrogen atom is $5.3 \times 10^{-11} \ m$. The radius of the fourth allowed orbit of the hydrogen atom is: (in $Å$)

Speed of electron in its $1^{st}$ Bohr's orbit is given by $2.18 \times 10^6 \ m/s$. If the time period of electron in $n^{th}$ orbit is measured as $4.10 \ fs$,the value of $n$ is

$A$ light of energy $12.75 \; eV$ is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is $\frac{x}{\pi} \times 10^{-17} \; eVs$. The value of $x$ is $........$ (use $h=4.14 \times 10^{-15} \; eVs$)