THE NATURE OF THE ATOM
REASONING AND SOLUTION
A tube is filled with atomic hydrogen at room
temperature. Electromagnetic radiation with a continuous spectrum of wavelengths,
including those in the Lyman, Balmer, and Paschen series, enters one end of the tube and
leaves the other end.
The exiting radiation is found to contain absorption lines.
At room temperature, most of the atoms of atomic hydrogen contain electrons that are in
the ground state (
= 1) energy level.
Since the radiation contains a continuous spectrum of
wavelengths, it contains photons with a wide range of energies (
particular, it will contain photons with energies that are equal to the energy difference
between the atomic states in the Lyman series. When the radiation is incident on the atoms
in the tube, these photons are absorbed by the electrons.
When a photon, whose energy is
equal to the energy difference for a transition in the Lyman series, is absorbed by a ground
state electron, that electron will make a transition to a higher energy level.
Every photon of
this energy will be absorbed by a ground state electron and cause a transition.
wavelength of radiation that corresponds to that particular photon energy will, therefore, be
removed from the radiation.
When the radiation is analyzed, the wavelengths that
correspond to transitions in the Lyman series will be absent.
Since most of the atoms in the
tube are in the ground state (
= 1), the electron populations in the
= 2 and
= 3 states are
Therefore, any absorption lines resulting from Balmer or Paschen
transitions will be extremely weak.
When the radiation is analyzed, the only predominant
absorption lines in the exiting radiation will correspond to wavelengths in the Lyman series.
REASONING AND SOLUTION
Refer to the situation described in Conceptual Question
Suppose the electrons in the atoms are mostly in excited states.
Most of the electrons are
in states with
2; therefore, Balmer and Paschen series transitions will occur, and the
absorption lines in the exiting radiation will correspond to wavelengths in the Balmer and
Since there are relatively few electrons in the ground state, only a relatively
few number of photons that correspond to wavelengths in the Lyman series will be
Most of the "Lyman photons" will remain in the radiation; therefore, the exiting
contain absorption lines that correspond to wavelengths in the Lyman
Although the absorption lines that correspond to transitions in the Lyman series are
not present, there will be more absorption lines in the exiting radiation compared to the
situation when the electrons are in the ground state, because absorption lines corresponding
to both the Balmer and Paschen series will be present.