Question

The Width of Spectral Lines: The average time after excitation at which a group of atoms radiate is called the lifetime, t, of an excited state. Due to Heisenberg uncertainty principle, the excited state energy has a corresponding uncertainty of DE, which is responsible for the width of spectral lines known as natural linewidth (natural broadening).

1. If t = 1.0´10^-8 s, calculate the energy uncertainty of the excited sate.
2. Compute the natural linewidth Df of light due to transition from this excited state to the ground state.
3. If the wavelength of the spectral line in this process is 500 nm, find the fractional broadening Df/f.
4. Calculate the linewidth Dl of the same spectral line.
5. Use the emitted photon wavelength of 500 nm, estimate the recoil momentum of the atom.

Answer 1