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Quantum Mechanics}Two-State Systems


Recall the mnemonic for remembering what a LASER is---Light Amplified Stimulated Emission Radiation.

A laser consists of two states, with a metastable-state in between the top and bottom state. Initially, one has all the atoms in the ground-state. But, photons come in to excite the atoms (through absorption), and the atoms jump into the top state; this is called a population inversion, as the ground-state atoms are now mostly in the top ``inverted" state. More photons come in to excite these already excited atoms, but instead of absorption, emission occurs, and the atoms jump to a lower meta-stable state while emitting photons (in addition to the incident photons). The atoms stay in this metastable state due to selection rules, where a transition back to the ground-state is forbidden.

One doesn't need to know all that to solve this problem. Instead, merely the idea of a laser requiring two main states and a metastable state in between would suffice. Since the question gives the bottom state as n=1 and top state as n=3, one deduces that the metastable state must be n=2, as in choice (B).

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Comments
hanin
2009-09-30 02:46:12
So if the transition is, for example, n=1 to n=4 then n=2 and n=3 have to be metastable?NEC
casaubon
2008-10-09 00:02:30
So I still don't get links on this site. Shows up fine in the preview. Anyways,

http://idol.union.edu/malekis/ESC24/Seyffie%27s%20Pages/Quantum%20Applications/threelevelatom.gif
NEC
madfish
2007-10-30 17:59:51
I don't understand why the system must have an n=2 level, the selection rules do not forbid the electron from jumping straight from n=1, l=0, m=0 to say n=3, l=1, m=0rnwithout ever touching the n=2
Ethan
2008-10-08 19:50:28
I believe the explanation goes as follows: in order for a laser too work, ie amplify the light put in, there must be an excess of electrons in the high energy state. N(n=3)>N(n=1). If n=2 were not metastable then it would not be possible to maintain this excess concentration in n=3, as the electrons would fill up the n=1 level too quickly.

In multiple gas lasers (I think the most common) the active gas need not have any metastable state.
casaubon
2008-10-09 00:01:58
Almost. The excess population exists at n=2 (the metastable state). The laser line is the n=2 to n=1 transition. See " target="_blank">http://idol.union.edu/malekis/ESC24/Seyffie%27s%20Pages/Quantum%20Applications/threelevelatom.gif">See this figure.

NEC
Richard
2007-09-28 16:45:33
Sorry to be punctilious, but "Light Amplification by Stimulated Emission" is hardly a mnemonic. It is an acronym. Do you have to remember that PHRASE to remember the word LASER?NEC

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