In which transition is one quantum of energy emitted?

Find the ionization energy and the wavelength of the photon emitted for a hydrogen atom transition from $n_1 = 2$ to $n_2 = \infty$.

One energy difference between the states $n = 2$ and $n = 3$ is $E \ eV$,in a hydrogen atom. The ionization potential of the $H$ atom is ............. $E$.

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.

The energy of an electron in a hydrogen atom when present in $n=1$, $n=2$, and $n=3$ will be in the ratio of:

When atoms are bombarded with alpha particles,only a few in a million suffer deflection,while others pass through undeflected. This is because: