A hypothetical atom has two energy levels, with a transition wavelength between them of 580 nm. In a particular sample at 300 K, 4.0 * 10^20 such atoms are in the state of lower energy. (a) How many atoms are in the upper state, assuming conditions of thermal equilibrium? (b) Suppose, instead, that 3.0*10^20 of these atoms are “pumped” into the upper state by an external process, with 1.0 * 10^20 atoms remaining in the lower state. What is the maxi-mum energy that could be released by the atoms in a single laser pulse if each atom jumps once between those two states (either via absorption or via stimulated emission)?

Bernard Boyer 2022-07-17 Answered
A hypothetical atom has two energy levels, with a transition wavelength between them of 580 nm. In a particular sample at 300 K, 4.0 10 20 such atoms are in the state of lower energy. (a) How many atoms are in the upper state, assuming conditions of thermal equilibrium? (b) Suppose, instead, that 3.0 10 20 of these atoms are “pumped” into the upper state by an external process, with 1.0 10 20 atoms remaining in the lower state. What is the maxi-mum energy that could be released by the atoms in a single laser pulse if each atom jumps once between those two states (either via absorption or via stimulated emission)?
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Answers (2)

Lillianna Mendoza
Answered 2022-07-18 Author has 16 answers
a) The upper level as level 1 and lower level as 2
Using
N 1 = N 2 e h c / λ K T = ( 4.0 × 10 20 ) e x p ( 1240 e V n m 580 n m ( 8.62 × 10 5   e V / K ) 300   K ) = 5.0 × 10 15 1
Thus, practically no electron occupies the upper level
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Lorelei Patterson
Answered 2022-07-19 Author has 6 answers
(b) The maximum energy
The expression for the maximum energy is
E m a x = ( N 1 N 2 ) E p h o t o n = ( 3.0 × 10 20 1.0 × 10 20 ) h c λ = ( 2.0 × 10 20 ) ( 6.63 × 10 34   J s ) ( 3 × 10 3   m / s ) 580 × 10 9   m = 68.58   J
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