Find out the distance between the $2^{nd}$ and $3^{rd}$ orbit of the $H^{-}$ ion.

If the ionization energy of $He^{+}$ is $8.68 \times 10^{-18} \ J$,then the energy of $Be^{3+}$ ion in the second orbit is:- ($Z$ of $Be = 4$)

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.

Threshold frequency,$v_0$ is the minimum frequency which a photon must possess to eject an electron from a metal. It is different for different metals. When a photon of frequency $1.0 \times 10^{15} \ s^{-1}$ was allowed to hit a metal surface,an electron having $1.988 \times 10^{-19} \ J$ of kinetic energy was emitted. Calculate the threshold frequency of this metal. Show that an electron will not be emitted if a photon with a wavelength equal to $600 \ nm$ hits the metal surface.

What transition in the hydrogen spectrum has the same wavelength as the Balmer transition,$n=4$ to $n=2$,of the $He^{+}$ spectrum?

In astronomical observations,signals observed from the distant stars are generally weak. If the photon detector receives a total of $3.15 \times 10^{-18} \, J$ from the radiations of $600 \, nm$,calculate the number of photons received by the detector.