The kinetic energy of the electron in an orbit of radius $r$ in a hydrogen atom is ($e =$ electronic charge).

An electron revolving in the $n^{\text{th}}$ Bohr orbit has a magnetic moment $\mu_n$. If $\mu_n \propto n^x$,the value of $x$ is:

In a hypothetical system,a particle of mass $m$ and charge $-3q$ is moving around a very heavy particle having charge $q$. Assuming Bohr's model to be true for this system,the orbital velocity of mass $m$ when it is nearest to the heavy particle is:

$13.6 \text{ eV}$ energy is required to separate a hydrogen atom into a proton and an electron. If the orbital radius of an electron in a hydrogen atom is $5.3 \times 10^{-11} \text{ m}$, then the velocity of the electron is . . . . . . .

The $21\, cm$ radio wave emitted by hydrogen in interstellar space is due to the interaction called the hyperfine interaction in atomic hydrogen. The energy of the emitted wave is nearly

The ratio of the area of the first excited state to the ground state orbit of a hydrogen atom is: