GREPhysics.NET: GR8677 #45

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chrisfizzix
2008-10-03 12:45:53

This problem bugged me a lot, mostly because I've been doing X-ray scattering problems in Solid State for several weeks now and had forgotten that elastic scattering didn't always imply that | $\vec{k}$ | = | $\vec{k'}$ |...

< / whining >

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Andresito
2006-03-16 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
2006-07-18 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.

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jax
2005-12-02 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
2007-02-22 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
2008-09-01 00:32:20

Try this.

All you need to know is
$p=h/\lambda$
and
$E=\bar{h}w=hc/\lambda$
From the conservation of momentum and energy, we have

$m_pv$ ~ $\frac{h}{\lambda}$

$\frac{hc}{\lambda}=\frac{hc}{\lambda'}+\frac{1}{2}m_pv^2$

P.S. You may find out these two arguments by drawing yourself a simple sketch of vectors.

Substitution (1) into (2)
we have

$\frac{\lambda^2}{\lambda}-\frac{\lambda^2}{\lambda'}=\frac{h}{m_pc}$

then, suppose $\lambda'=\lambda+\kappa$

$\lambda^2(\frac{1}{\lambda}-\frac{1}{\lambda+\kappa})=\frac{h}{m_pc}$

then

$\lambda^2(\frac{\lambda+\kappa-\lambda}{\lambda(\lambda+\kappa)}})=\frac{h}{m_pc}$

thus
$\kappa = \frac{h}{m_pc}$
which $\kappa$ 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 $\lambda$ and $\lambda'$ is $\underline{independent}$ in both sides of the equation. (How wonderful if you can subtract $\lambda$ from $\lambda'$ . That is the answer. The only difficulty is that they all at denomintors) Thus, you want to write $\lambda'$ as something big + something small. Then you can cancell the big ones on both side and the small one-the answer-remain.

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physicsDen
2005-11-09 21:42:11

how can the momentum of the PROTON have momentum with the speed of light???

yosun
2005-11-09 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

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physicsDen
2005-11-09 21:40:52

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physicsDen
2005-11-09 21:40:42

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