GR8677 #45


Problem



Quantum Mechanics}Compton Effect
This problem can be solved via the Compton Effect equation , where is the angle of the scattered photon and is the socalled Compton Wavelength. In this case, since the particles are protons, one has .
Since the photon scatters off at 90 degrees, the equation simplifies to . This is the increase in wavelength, as in choice (D).
To a certain degree, one can handwave this problem via the following method:
Recall the de Broglie relation,
, where is the wavelength, is the momentum and is Planck's constant.
The momentum of the proton is , thus .


Alternate Solutions 
OptimusPrime 20170408 02:27:42  (A) and (B) are maybes so far.\r\n(C)  No, we are dealing with PROTONS instead of the usual electrons. So the mass of the electron shouldn\'t come into play at all.\r\n(D)  Maybe.\r\n(E)  No, since after this collision the photon must lose energy. Recall that higher frequency means higher energy. So if we are losing energy, that means our frequency has decreased, and since frequency and wavelength are inversely related, the wavelength has increased. \r\n\r\nIf you remember the Compton equation then you\'ll find as Yosun wrote that change in wavelength equals the Compton wavelength. But, where can we extract any numbers from that?! We can\'t, so (A) and (B) are out.\r\n\r\nThat leaves (D). On top of that, (D) has the correct dimensions. [h/mc] = (M*(L^2) / T) / (M*L / T) = L. Length as in wavelength.  

Comments 
OptimusPrime 20170408 02:27:42  (A) and (B) are maybes so far.\r\n(C)  No, we are dealing with PROTONS instead of the usual electrons. So the mass of the electron shouldn\'t come into play at all.\r\n(D)  Maybe.\r\n(E)  No, since after this collision the photon must lose energy. Recall that higher frequency means higher energy. So if we are losing energy, that means our frequency has decreased, and since frequency and wavelength are inversely related, the wavelength has increased. \r\n\r\nIf you remember the Compton equation then you\'ll find as Yosun wrote that change in wavelength equals the Compton wavelength. But, where can we extract any numbers from that?! We can\'t, so (A) and (B) are out.\r\n\r\nThat leaves (D). On top of that, (D) has the correct dimensions. [h/mc] = (M*(L^2) / T) / (M*L / T) = L. Length as in wavelength.   a62 20160920 01:19:12  I don\'t know the Compton equation off the top of my head, but I got this right easily simply because I remembered that the wavelength does change and the change is independent of the initial wavelength (I think that maybe that\'s important because it\'s predicted by the photon model, but not the classical wave model of light?). The wavelength shift is a result of a collision, so of course the mass in the equation is the mass of whatever the photon is colliding with. That narrows it down to only one answer.   849444209 20131016 06:29:20  记公式不就行了，这题太尼玛简单了
FloweryFlood 20141005 04:49:25 
Why are you always trying to be such arrogant？
What makes you feel like you are the only person who remember the equation:

godkun@yeah.net 20160630 15:46:27 
Don\'t be obnoxious!\r\n\r\n\r\n

  gigadan 20130923 20:52:26  How does a Photon have rest mass?
I was stumbled on C or D but D makes nonsense to me.
llama 20131016 19:10:10 
It doesn't, pRotons do :). D is the only one that deals with values relevant to the problem (well it's plausible that the fine structure constant is involved, but not immediately obvious)

  chrisfizzix 20081003 12:45:53  This problem bugged me a lot, mostly because I've been doing Xray scattering problems in Solid State for several weeks now and had forgotten that elastic scattering didn't always imply that  = ...
< / whining >   Andresito 20060316 21:29:44  One should look at the important preposition "the wavelenght of scattered photons is INCREASED by"
This narrows the choices to (C) and (D), and one should choose (D) since it involves protons. The last argument merely goes as intuition.
ben 20060718 16:59:11 
this does not necessarily rule out (A) and (B) since lambda/137 and lambda/1836 are both positive numbers and adding them to the wavelength would still increase the wavelength. there is nothing inherently wrong with saying that the wavelength is increased by lambda/137. e.g., if the wavelength is 1 then increasing it by lambda/137 would give a wavelength of 1+1/137 which is greater than the original wavelength. no problem with that.

  jax 20051202 11:13:45  One thing I hate about the physics GRE is that I don't have time to derive things like the Compton equation from scratch... so the alternative is memorizing it but I am not very good at that. So if I happen to forget the equation, what do I do? Just skip the question, or spend 5 or 6 minutes deriving the equation.
My physics program never put the emphasis on what you could memorize so this type of exam is very hard for me to study for...
yosun 20070222 15:23:21 
The Compton Equation is actually one of those things you should know... (some even consider it a fundamental equation of modern physics) But, you can always derive it using conservation of momentum/energy.

jw111 20080901 00:32:20 
Try this.
All you need to know is
and
From the conservation of momentum and energy, we have
~
P.S. You may find out these two arguments by drawing yourself a simple sketch of vectors.
Substitution (1) into (2)
we have
then, suppose
then
thus
which is the increasing of wave length
Does this solve your problem? This is how I do this question.
The key idea of this method is that when writing down the energy conservation you can see both and is in both sides of the equation. (How wonderful if you can subtract from . That is the answer. The only difficulty is that they all at denomintors) Thus, you want to write as something big + something small. Then you can cancell the big ones on both side and the small onethe answerremain.

  physicsDen 20051109 21:42:11  how can the momentum of the PROTON have momentum with the speed of light???
yosun 20051109 22:21:48 
sorry physicsDen. that was a poor attempt to derive the compton effect from scratch. the standard method for solving that (i.e., the usual compton effect equation) has been posted. thanks for pointing this out. on the same tangent, you might be interested in:
http://grephysics.net/disp.php?yload=prob&serial=2&prob=67

  physicsDen 20051109 21:40:52    physicsDen 20051109 21:40:42   

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