Talk:Absorption spectrum
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[edit] Conservation of momentum
"However, this is emitted in all directions, not just in the direction in which the electromagnetic radiation was originally travelling."
- How does this conserve momentum? lysdexia 23:42, 22 Nov 2004 (UTC)
- In the case of annihilation, conservation of momentum requires the two emitted photons to travel in opposite directions. So I would assume that in this case, whatever momentum the photon has, the atom's momentum changes by the same amount in the opposite direction. --Shinglor 10:34, 28 August 2007 (UTC)
[edit] The word inverse appears in the meaning which is absent in wikipedia.
In mathematics, the Inverse element of an element x in a binary operation with identity element e is 
so that 
Also, Inverse function of function 
is function 
such that 
.
None of this cases apply to the spectra of absorption and emission.
Perhaps, the author means that spectrum 
of absorption is related to the spectrum 
of emissioon with 
, where 
and 
are smooth (slow) functions of frequency (or wavenumber, or wavelenght).
If there is any way to express this in wikipedia-English?
[edit] These gaps occur despite the re-emission of photons because the re-emitted photons are equally likely to travel in all directions, and it is statistically unlikely to travel along the original path to
Such explanation is unacceptable. Let us see why
The Fig. 1 shows a lamp emitting a continuos spectrum that falls upon a prism, and the prism projecting a continuous spectrum in the screen.
FIG.1: http://www.geocities.com/ciencia2mil/DANIELcontinuous-spectrum.jpg
Among all the frequencies emitted by the lamp, obviously there are photons emitted in that same specific frequency emitted by the Na atoms. Let’s call Ph(Na) such photons emitted in the specific frequencty of Na atoms, emitted by the lamp The Fig.1 shows where the Ph(Na) spectrum falls upon the screen.
Consider a prism with area s=10cm2 = 10-3m2
Suppose that it’s “Z” the total quantity of photons Ph(Na) emitted by the lamp. The area S of the sphere with radius R = 1m is: S= 4πR2 = 12,5
Therefore the quantity of emitted Ph(Na) photons emitted by the lamp that falls upon the prims is:
Qe = Z.s/S = Z.(10-3 / 12,5) ~ Z.10-4 = Z/10000
And obviously such quantity Qe = Z/10000 of photons Ph(Na) is shinning, otherwise the spectrum would not be continuous.
Now consider the Fig.2, where we introduce the vapour of Na
FIG. 2: http://www.geocities.com/ciencia2mil/DANIELabsorption-spectrum.jpg
Note that now the distance between the prism and the lamp is 15cm, and so the distance between the prism and the atoms of Na [which re-emits the absorbed photons Ph(Na) ] is approximatelly 10cm).
A quantity Z/2 emitted by the lamp is spread in the Side A of the line that divides the lamp, and a quantity Z/2 is emitted spread in the side B. Obviously we are interested in photons emitted in the Side B.
Let’s call Re-Ph(Na) the photons re-emitted by the Na atoms. Now, with R= 0,1m:: S = 4πR2 = 12,5x10-2m2
The quantity of photons Re-Ph(Na) re-emitted by the Na atoms that falls upon the prism is:
Qre = (Z/2).s/S = 0,5Z.(10-3 / 12,5x10-2) = 0,5Z/125 = Z/250
Then now compare:
Qe = Z/10000 is the quantity of photons Ph(Na) emitted by the lamp, which falls upon the prism, and they are shinning in the continous spectrum of the Fig. 1.
Qre =Z/250 is the quantity of photons Re-Ph(Na) emiited by the atoms Na of the vapour of sodium, which falls upon the prism in the Fig. 2
CONCLUSION:
As a quantity Qe = Z/10000 of emitted photons are able to produce a shinning line in the screen...
... then why a quantity Qre = Z/250 of re-emitted photons are unable to produce a shinning line in the screen?
Therefore it is absurd to claim that QM is able to explain the absorption spectrum by alleging that the re-emitted photons does not fall upon the prism
