7.13. Consider the atomic system shown below being irradiated by an external wave tuned to the center of the 2 1 transition with 1 being the ground state. The wave pumps the atoms from 1 to 2 and also stimulates the atoms back to 1 from 2. In addition, the atoms in state 2 decay back to 1 by spontaneous emission and/or by other processes with a rate given by (T). The total density of atoms is [N]. Assume o 10-14 cm² (a) Formulate the rate equations for the two states in terms of the intensity of the external wave, the stimulated emission cross section, the frequency hv= E₂ E₁, T, and the degeneracies of the states (82, 81).

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7.13. Consider the atomic system shown below being irradiated by an external wave tuned
to the center of the 2→ 1 transition with 1 being the ground state. The wave pumps
the atoms from 1 to 2 and also stimulates the atoms back to 1 from 2. In addition, the
atoms in state 2 decay back to 1 by spontaneous emission and/or by other processes
with a rate given by (T). The total density of atoms is [N]. Assume o 10-14 cm²
(a) Formulate the rate equations for the two states in terms of the intensity of
the external wave, the stimulated emission cross section, the frequency hv=
E₂-E₁, T, and the degeneracies of the states (g2, 81).
References and Suggested Readings
(b) What would be the population ratio N₂/N, if the intensity of the external wave
were infinite?
(c) What must be the intensity to make the population ratio N₂/N₁ equal to 1/2?
(d) If the ambient temperature were such that kT= 208 cm and the intensity
were zero, what is the steady state population ratio №₂/N₁?
E₂= 11,735 cm: 82=4
2
T= 1 μsec
Pump
205
E₁=0:g₁=2
Transcribed Image Text:7.13. Consider the atomic system shown below being irradiated by an external wave tuned to the center of the 2→ 1 transition with 1 being the ground state. The wave pumps the atoms from 1 to 2 and also stimulates the atoms back to 1 from 2. In addition, the atoms in state 2 decay back to 1 by spontaneous emission and/or by other processes with a rate given by (T). The total density of atoms is [N]. Assume o 10-14 cm² (a) Formulate the rate equations for the two states in terms of the intensity of the external wave, the stimulated emission cross section, the frequency hv= E₂-E₁, T, and the degeneracies of the states (g2, 81). References and Suggested Readings (b) What would be the population ratio N₂/N, if the intensity of the external wave were infinite? (c) What must be the intensity to make the population ratio N₂/N₁ equal to 1/2? (d) If the ambient temperature were such that kT= 208 cm and the intensity were zero, what is the steady state population ratio №₂/N₁? E₂= 11,735 cm: 82=4 2 T= 1 μsec Pump 205 E₁=0:g₁=2
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