If the speed of an electron in the Bohr's first orbit of a hydrogen atom is $x$,the speed of the electron in the third Bohr's orbit is:

The wave numbers of three spectral lines of $H$ atom are considered. Identify the set of spectral lines belonging to the Balmer series. ($R =$ Rydberg constant)

Explain: Photoelectric effect.

If '$X$' is the ionization energy of hydrogen,then the energy required for the excitation of a $Li^{2+}$ electron from the $2^{nd}$ excited state to the $5^{th}$ excited state is:

If an electron transitions from $n = 5$ to $n = 2$ in a hydrogen spectrum,identify the series and the region of the spectrum.

Lifetimes of the molecules in the excited states are often measured by using pulsed radiation source of duration nearly in the nanosecond range. If the radiation source has the duration of $2 \, ns$ and the number of photons emitted during the pulse source is $2.5 \times 10^{15}$,calculate the energy of the source.