Download LASERS - PROBLEMS Electron mass = 9.11 x 10–31kg, electron

LASERS - PROBLEMS
Electron mass = 9.11 x 10–31kg,
electron charge = 1.60 x 10–16C,
Boltzmann constant = 1.38 x 10–23J/K, Planck’s constant = 6.63 x 10–34J.s
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HRK 5e p1100 E48.34
A hypothetical atom has only two atomic levels, separated in energy by 3.2
eV. In the atmosphere of a star there are 6.1 x 1019 of these atoms / m3 in
the excited state and 2.5 x 1021 / m3 in the ground state. Calculate the
temperature of the star’s atmosphere.
(Answer: 9990 K)
HRK 5e p1100 E48.31
A hypothetical atom has energy levels evenly spaced by 1.2 eV in energy.
Calculate the ratio of the number of atoms in the 13th excited state to the
number in the 11th excited state at 2000 K.
(Answer: 9.1 x 10–7)
HRK 5e p1100 E48.33
A hypothetical atom has two energy levels with a transition wavelength of
582 nm. In such a sample at 300 K, 4 x 1020 atoms re there in the lower
state. (a) How many occupy the upper state under conditions of thermal
equilibrium? (b) Suppose, instead, that 3.0 x 1020 atoms are pumped into
upper state, with 1.0 x 1020 remaining in the lower state. How much energy
could be released in a single laser pulse?
(Answer: 0, 102 J)
HRK 5e p1095 SP48.7
A three level laser emits light of wavelength 550 nm. (a) What is the rate of
population of the upper level (E2) to that of the lower level (E1) in laser
transition, at 300 K? (b) At what temperature the ratio of the population of
E2 to that of E1 becomes half? (c) At what negative temperature the
population of the upper level exceeds that of the lower by 10%?
(Answer: 1.3 x 10–38, 38000 K (hotter than Sun), –280000 K)
HRK 5e p1100 E48.28
A ruby laser emits a light of wavelength 694.4 nm. If a laser pulse is emitted
for 12.0 ps and the energy release per pulse is 150 mJ, (a) what is the
length of the pulse? (b) How many photons are there in each pulse?
(Answer: 3.6 mm, 5.24 x 1017)
HRK 5e p1100 E48.30
A He-Ne laser emits light of wavelength of 632.8 nm and has an output
power of 2.3 mW. How many photons are emitted each minute by this laser
when operating?
(Answer: 4.4 x 1017)
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HRK 5e p1096 SP48.8
A pulsed ruby laser emits a light of wavelength 694 nm and has a ruby rod of
6 cm length and 1 cm diameter. The ruby rod has Cr2O3 doped to an extent
of one molecule in every 3500 Al2O3 molecules. Assume 100% population
inversion at an instant and calculate the energy of the laser pulse when all
the Cr+3 ions in the metastable state come down to ground state. The
density of Al2O3 is 3700 kg/m3, the molar mass of Al2O3 is 102 g/mol.
(Answer: 17 J) (Good question)
HRK 5e p1100 E48.34
The mirrors in a laser form a cavity in which standing waves of laser light are
set up. In the vicinity of 533 nm (He-Ne laser), how far apart in wavelength,
are the adjacent allowed operating modes? The mirrors are 8.3 cm apart.
Show that the frequency shift for the adjacent modes is the reciprocal of the
travel time of light for one round trip between the mirrors. (Problem)
(Answer: 1.7 pm)
1. Solution for the third problem (b) is (n h c / wavelength)
2. Solution for the fifth problem (a) is LENGTH = VELOCITY OF LIGHT
MULTIPLIED WITH TIME FOR EACH PULSE (12 PICO Sec.)
3. Solution for the fifth problem (b) is ((n h c/ wavelength) = 150Mj )
4. Solution for the sixth problem was similar to that of fifth problem.
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