An electron in the ground state of the hydrogen atom has an orbital radius of $5.3 \times 10^{-11} \ m$,while that for the electron in the third excited state is $8.48 \times 10^{-10} \ m$. The ratio of the de Broglie wavelengths of the electron in the ground state to that in the third excited state is:

The time period of revolution of an electron in its ground state orbit in a hydrogen atom is $1.6 \times 10^{-16} \; s$. The frequency of revolution of the electron in its first excited state (in $s^{-1}$) is:

In a hydrogen atom,the binding energy of the electron in the $n^{th}$ state is $E_n$. Then,the frequency of revolution of the electron in the $n^{th}$ orbit is:

$A$ hydrogen-like atom has one electron revolving around a stationary nucleus. If the energy required to excite the electron from the $2^{nd}$ orbit to the $3^{rd}$ orbit is $47.2 \ eV$,find the atomic number of the given atom.

The speed of an electron in the orbit of a hydrogen atom in the ground state is

Experimentally it is found that $12.8 \, eV$ energy is required to separate a hydrogen atom into a proton and an electron. The orbital radius of the electron in this hydrogen atom is $\frac{9}{x} \times 10^{-10} \, m$. The value of $x$ is (Given: $1 \, eV = 1.6 \times 10^{-19} \, J$,$\frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \, Nm^2/C^2$,and electronic charge $e = 1.6 \times 10^{-19} \, C$)