Consider the spectral line resulting from the transition $n = 2 \rightarrow n = 1$ in the atoms and ions given below. The shortest wavelength is produced by:

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 $: 1$)

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?

Ratio of centripetal acceleration for an electron revolving in $3^{\text{rd}}$ orbit and $5^{\text{th}}$ Bohr orbit of hydrogen atom is

For $He^{+}$, a transition takes place from the orbit of radius $105.8 \ pm$ to the orbit of radius $26.45 \ pm$. The wavelength (in $nm$) of the emitted photon during the transition is. . . . .
[Use: Bohr radius, $a_0=52.9 \ pm$; Rydberg constant, $R_H=2.2 \times 10^{-18} \ J$; Planck's constant, $h=6.6 \times 10^{-34} \ J \ s$; Speed of light, $c=3 \times 10^8 \ m \ s^{-1}$]

If the speed of an electron of a hydrogen atom in the ground state is $2.2 \times 10^6 \ m/s$,then its speed in the third excited state will be