Page 438 - Schaum's Outline of Theory and Problems of Applied Physics

CHAP. 34] ATOMIC PHYSICS 423

contains all frequencies). These atoms will absorb only light of frequencies that correspond to particular energy
differences; these are the differences that correspond to transitions from the ground state to excited states. The
excited atoms then fall back to their ground states, reradiating light as they do so. However, since the reradiation
occursrandomlyinalldirections,onlyasmallfractionofthereradiatedlightisinthedirectionoftheoriginalbeam.

THE LASER
A laser is a device that produces an intense beam of monochromatic, coherent light from the cooperative radiation
of excited atoms. The light waves in a coherent beam are all in phase with one another, which greatly increases
their effectiveness. A laser beam is virtually nondivergent and hence remains as a narrow pencil of light even
after traveling a large distance.
The word laser stands for light amplification by stimulated emission of radiation. In a laser, atoms of
a particular kind are raised to metastable (temporarily stable) states of energy hf , which are excited states
of relatively long lifetimes. Radiation of frequency f induces the excited atoms to emit photons of the same
frequency and thereby to return to their ground (normal) states so that a small amount of initial radiation can be
greatly amplified.

SOLVED PROBLEM 34.8

Describe two mechanisms by which the atoms of a gas can be excited so that they emit light whose
frequencies make up the characteristic line spectrum of the element involved.

(1) One mechanism is a collision with another atom, as a result of which some of their kinetic energy becomes
excitation energy within one or both atoms. The excited atoms then lose this energy by emitting one or more
photons. In an electric discharge in a gas, for instance in a neon sign or a sodium-vapor highway lamp, an
electric field accelerates electrons and ions to velocities sufficient for atomic excitation.
(2) Another mechanism is the absorption by an atom of light for which hf is just right to raise the atom from
its ground state to one of its excited states. If white light is directed at the gas, photons of those energies that
correspond to such transitions are absorbed. When the energy is reradiated, all the possible transitions from the
highest excited state reached show up in the emitted light.

SOLVED PROBLEM 34.9
A proton and an electron come together to form a hydrogen atom in its ground state. Under the assumption
that a single photon is emitted in this process, what is its frequency?
The energy of a hydrogen atom in its ground state is −13.6eV =−2.13 × 10 −18 J. Hence 2.18 × 10 −18 Jof
energy must be given off when the atom is being formed. If a single photon is emitted, its frequency is found from
E = hf to be
E 2.18 × 10 −18 J 15
f = = = 3.3 × 10 Hz
h 6.63 × 10 −34 J·s

SOLVED PROBLEM 34.10
Of the following transitions between energy levels in a hydrogen atom, which one involves (a) the emis-
sion of the photon of highest frequency, (b) the emission of the photon of lowest frequency, (c) the
absorption of the photon of highest frequency, (d) the absorption of the photon of lowest frequency? The
transitions are n = 1to n = 2; n = 2to n = 1; n = 2to n = 6; and n = 6to n = 2.
In general, photon emission occurs during a transmission to a state of lower n, and photon absorption occurs
during a transition to a state of higher n. By inspecting the energy level diagram of hydrogen (Fig. 34-1), we see that
the energy difference between the n = 1 and n = 2 levels is greater than that between the n = 2 and n = 6 levels.
Hence the answers are as follows: (a) n = 2to n = 1; (b) n = 6to n = 2; (c) n = 1to n = 2; (d) n = 2to n = 6.