In stars the Pickering series is found in the spectrum. It is emitted when the electron in jumps from higher levels to the level with . We have to show that (a) the wavelengths of the lines in this series are given by

in which . (b) We have to calculate the wavelength of the first line in this series and of the series limit. (c) We have to find the region of the electromagnetic spectrum in which this series occurs.

Solution:             Click For PDF Version

(a)

In the Bohr’ model the energies of hydrogen like atom are given by

The Rydberg constant R can be expressed in terms of the fundamental constants as

where Z is the charge of the nucleus and is the fine structure constant,

For atom and

Pickering series corresponds to transitions from states with to the state with . Thus the wavelengths of radiation which form Pickering series will be given by

(b)

The wavelength of the first line in the Pickering series will correspond to transition from the state with to . We find

We next calculate the value of R

Therefore,

Wavelength of the series limit will correspond to .

We get

(c)

The spectrum of wavelengths in the Pickering series, therefore, occurs in the ultraviolet region extending to visible region.