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

The kinetic energy of an electron in the first Bohr orbit of the hydrogen atom is $...... eV$.

$A$ particular hydrogen-like ion emits radiation of frequency $2.92 \times 10^{15} \text{ Hz}$ when it makes a transition from $n=3$ to $n=1$. The frequency in $\text{Hz}$ of radiation emitted in the transition from $n=2$ to $n=1$ will be: (in $\times 10^{15}$)

The ionisation potential of $H$-atom is $13.6 \, eV$. When it is excited from the ground state by monochromatic radiation of $970.6 \, \mathring{A}$,the number of emission lines will be (according to Bohr's theory):

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 $n >> 1$.

In a hydrogen-like atom,the velocity of an electron in the second orbit is $v$. What will be the velocity of the electron in its fifth orbit?