Name: Solutions
Introduction to Lasers
Module 1-5
Due: __________
2015-2016
Instructions: Do every problem. For full credit, be sure to show all your work. The point is to show me that you know HOW to do the problems, not that you can get the right answer, possibly by accident.
1. Define the following terms: a. Joule – standard unit of measurement for energy in MKS system b. Erg – standard unit of measurement for energy in CGS system c. Electron volt – unit of energy equal to 1.6×10 −19 joules d. Reciprocal centimeter – unit of measurement for the wavenumber e. Wave number - the reciprocal of the wavelength f. Atomic lifetime - the time required for half of the atoms initially in that state to make a
downward transition without the benefit of outside influence g. Metastable state - excited states that have longer than average atomic lifetimes h. Radiationless transition - a downward transition that does not result in the emission of a photon
2. Calculate the equivalent energy of each of the values given to complete the following table.
Joules
3.0 x 10 -19
2.7 x 10 -19
3.97 x 10 -19
Ergs
3.0 x 10 -12
2.7 x 10 -12
3.97 x 10 -12
Electron Volt
1.87
1.69
2.48
3. Calculate the frequency, the wave number, and the energy (in eV) of the following wavelengths of light: cm -1
15,100
13,600
1.08
Wavelength
450 nm
6.32 10 -7 m
1.15 um
Frequency (Hz)
6.67 10
4.75 10
2.61 10
14
14
14
Wave number (cm -1 )
2.22 10 4
1.58 10 4
0.87 10 4
Energy (eV)
2.76
1.96
1.08

Name: Solutions
Introduction to Lasers
Module 1-5
Due: __________
2015-2016
4. Describe each of the following processes. For items b and c, include the initial conditions necessary. a. Spontaneous emission of a photon by an atom - an atom in an excited state relaxes to a lower energy level by giving off a photon with energy equal to the difference in energy of the two levels. b. Absorption of a photon by an atom - a photon with energy Ehigher – Elower interacts with an atom in the lower energy level; the photon ceases to exist and the atom is excited to the higher energy level. c. Stimulated emission of a photon by an atom - a photon with energy E higher
– E lower interacts with an atom in the higher energy level; the atom relaxes into the lower energy level while giving off its energy in the form of a photon; the new photon is identical in every way to
the original photon.
5. Draw and label diagrams that illustrate the following spectra: a. Emission spectrum of an atomic gas at low pressure b. Absorption spectrum of a solid
6. Describe the relation between atomic lifetime and the intensity of spectral emission lines.
Stronger lines in an emission spectrum of a gas are the result of the most probable transitions from energy states having short atomic lifetimes.
Weaker lines are the result of the less probable transitions and those having longer lifetimes.

Name: Solutions
Introduction to Lasers
Module 1-5
Due: __________
2015-2016
7. Explain the Doppler broadening of a spectral line in a gas. A stationary atom emits light of wavelength λ
0
. If an atom is moving away, then the wavelength emitted is slightly longer. If an atom is moving toward, then the wavelength emitted is slightly shorter. This is Doppler
Broadening.