Consider an electron moving in the first Bohr orbit of a $He^{+}$ ion with a velocity $v_1$. If it is allowed to move in the third Bohr orbit with a velocity $v_3$, then indicate the correct $v_3: v_1$ ratio.

When $\alpha$-particles are sent through a thin metal foil,most of them go straight through the foil because

In $He^{+}$ ion,the energy of $2^{nd}$ orbit is $-13.6 \ eV/atom$. The kinetic energy of the same orbit for $He^{+}$ ion will be:

The Balmer series in the hydrogen spectrum corresponds to the transition from $n_1 = 2$ to $n_2 = 3, 4, ...$ This series lies in the visible region. Calculate the wave number of the line associated with the transition in the Balmer series when the electron moves to the $n = 4$ orbit. $(R_H = 109677 \ cm^{-1})$

The energy of the second excited state of the $Li^{2+}$ ion is ............... $eV$.

What are the frequency and wavelength of a photon emitted during a transition from $n=5$ state to the $n=2$ state in the hydrogen atom?