In hydrogen atoms, the radius of the smallest orbit of the electron is $a_0$. The radius of the third orbit is:

The electron in a hydrogen atom makes a transition from the $M$ shell to the $L$ shell. The ratio of the magnitudes of the initial to the final centripetal acceleration of the electron is:

$P$ is the probability of finding the $1s$ electron of a hydrogen atom in a spherical shell of infinitesimal thickness, $dr$, at a distance $r$ from the nucleus. The volume of this shell is $4\pi r^2 dr$. The qualitative sketch of the dependence of $P$ on $r$ is:

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:

The following statements are given about the hydrogen atom:
$A$. The wavelengths of the spectral lines of the Lyman series are greater than the wavelength of the second spectral line of the Balmer series.
$B$. The orbits correspond to circular standing waves in which the circumference of the orbit equals a whole number of wavelengths.

In the Bohr model of the hydrogen atom,let $R, v$,and $E$ represent the radius of the orbit,the speed of the electron,and the total energy of the electron,respectively. Which of the following quantities is proportional to the quantum number $n$?