The speed of the electron (in $ms^{-1}$) in the third orbit of a hydrogen atom is approximately (mass of electron $= 9.1 \times 10^{-31} \ kg$).

For a $H$-atom,what is the wavelength in $nm$ associated with the transition of an electron from an infinite energy level to the first energy level? (Rydberg constant = $1.097 \times 10^{7} \ m^{-1}$)

Positronium consists of an electron and a positron (a particle which has the same mass as an electron,but opposite charge) orbiting round their common centre of mass. Calculate the value of the Rydberg constant for this system.

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.

What is the number of photons of light with a wavelength of $4000 \ pm$ that provide $1 \ J$ of energy?

For any given series of spectral lines of atomic hydrogen,let $\Delta \bar{\nu} = \Delta \bar{\nu}_{\max} - \Delta \bar{\nu}_{\min}$ be the difference in maximum and minimum wavenumbers in $cm^{-1}$. The ratio $\Delta \bar{\nu}_{\text{Lyman}} / \Delta \bar{\nu}_{\text{Balmer}}$ is