Question

Compton Scattering

Answer 1

A photon with wavelength = 0.1385 nm scatters from an electron that is initially at rest. What must be the angle between the direction of propagation of the incident and scattered photons if the speed of the electron immediately after the collision is 8.90*10^6 m/s?

Hey @theEric I have this problem, and I'm sure I know how to solve it but I'm not getting the right number like here I'm using conservation of energy.

Answer 2

\[\frac{ hc }{ \lambda } =\frac{ hc }{ \lambda ' }+\frac{ 1 }{ 2 }mv^2\]

solving for lambda prime I get

\[\frac{ 2 \lambda h c }{ 2hc - mv^2 \lambda }\] but I get some weird answer for the wavelength here, thought you could check it out :P

Answer 3

\[\frac{ 2 (0.1385 \times 10^{-9}nm)(6.626 \times 10^{-34}Js)(3 \times 10^8 m/s) }{ ((2(6.626 \times 10^{-34})(3 \times 10^8 m/s))-((9.11 \times 10^{-34} kg)(8.90 \times 10^6 m/s)^2(0.1385 \times 10^{-9} nm)) }\]

Answer 4

Getting \[1.38503*10^{-10} m\] seems a bit wrong, think my algebra is wrong?

Answer 5

I haven't gone through the math yet, but that result that you got is for \(\lambda '\), right?

It looks like \(\lambda=\lambda'\)! Haha, is that what might be odd?

Answer 6

I don't know how much it should change, to be honest!

Answer 7

I agree with the algebra to get from your first equation to second, though!

Answer 8

\(m\) is the mass of the electron, right?
If so, then \(m\approx9.11\times10^{-31}\), rather than \(\times10^{-34}\). I don't know if that corrects it or not!

Answer 9

That could've just been a typo, also. They're very easy to make in these big \(\LaTeX\) equations.

Answer 10

Haha sorry for the late reply i went out for a sec and omg you're right thats the mass XD

Answer 11

Haha, np! Does that fix the issue? I didn't use a calculator yet.

Answer 12

i will check it in 5 min, just about to eat and I'll get back to ya :p, thank you eric that was a dumb mistake haha.

Answer 13

Np. It was an \(\color{green}{easy}\) mistake!

Answer 14

YAY it works now, thank you :D

Answer 15

You're welcome! I got 0.2770nm.

Answer 16

0.1421 nm

Answer 17

Check your brackets?

Answer 18

Haha, probably! Let me check!

Answer 19

I checked with my name and it agrees as well haha :P

http://www.wolframalpha.com/input/?i=%28%28%282%29%280.1385*10%5E%7B-9%7D%29%286.626*10%5E%7B-34%7D%29%283*10%5E8%29%29%2F%28%28%282%29%286.626*10%5E%7B-34%7D%29%283*10%5E8%29%29-%28%289.11*10%5E%7B-31%7D%29%288.9*10%5E6%29%5E2%280.1385*10%5E%7B-9%7D%29%29%29

Answer 20

I used your name which agrees for the most part!
http://www.wolframalpha.com/input/?i=%282*0.1385*10^%28-9%29*6.26*10^%28-34%29*3*10^8%29%2F%282*6.26*10^%28-34%29*3*10^8-9.11*10^%28-31%29*%288.9*10^6%29^2*0.1385*10^%28-9%29%29

Answer 21

Haha

Answer 22

Hehe, I fixed mine...

Answer 23

You're good :)

Answer 24

Thanks again for pointing that error out for me Eric hehe :P

Answer 25

No problem! :)