For principal quantum number $n = 3$,the possible values of orbital quantum number $l$ are

The radius of the first orbit in an $H$-atom is '$a_0$'. Then,the de-Broglie wavelength of the electron in the third orbit is: (in $\pi a_0$)

In the Bohr model of the hydrogen atom,the ratio of the periods of revolution of an electron in $n = 2$ and $n = 1$ orbits is: (in $: 1$)

Show that the first few frequencies of light that is emitted when electrons fall to the $n^{\text{th}}$ level from levels higher than $n$,are approximate harmonics (i.e.,in the ratio $1:2:3...$) when $n >> 1$.

The orbital acceleration of an electron is .........

Consider a hydrogen atom with its electron in the $n^{\text{th}}$ orbital. An electromagnetic radiation of wavelength $90 \ nm$ is used to ionize the atom. If the kinetic energy of the ejected electron is $10.4 \ eV$,then the value of $n$ is $(hc = 1242 \ eV \ nm)$.