Compton Effect, frequency question

[Kennedy111]

Homework Statement

An X-ray with a frequency of 3.74 x 10^20 Hz is incident on a thin piece of metal. The lower frequency X ray on the other side is observed deflected at 48°. What is the frequency fo the deflected X ray?

fi = 3.74 x 10^20 Hz
Deflected at 48°

Homework Equations

I'm not sure... I would guess..

Δλ= (h/mc)(1-cosθ)
E = hf
E = hc/λ
(hc/λ)=hf

The Attempt at a Solution

I really have no idea where to begin... If someone could just start me off that would be awesome :) This is my attempt anyway..

Ei = hf
= (6.63 x 10^-34 Js)(3.74 x 10^20 Hz)
= 2.47962 x 10^-13 J

E = hc/λ
λ= hc/E
= (6.63 x 10^-34 js)(3.00 x 10^8 m/s) / (2.47962 x 10^-13 J)
= 8.02139037 x 10^-13 m

Δλ = λf - λi
λf = Δλ + λi
= ((6.63 x 10^-34 Js) / (9.11 x 10^-31 kg)(3.00 x 10^8 m/s))(1- cos48) + 8.02139037 x 10^-13 m
=4.78097437 x 10^-12 m

Ef = hc/λ
=(6.63 x 10^-34 Js)(3.00 x 10^8 m/s) / (4.78097437 x 10^-12 m)
=4.16023983 x 10^-14 J

E = hf
f = E/h
= (4.16023983 x 10^-14 J) / (6.63 x 10^-34 Js)
= 6.274871536 x 10^-19 Hz

Yeah... I don't think this is right..

Please help!

 

[TSny]

Ei = hf
= (6.63 x 10^-34 Js)(3.74 x 10^20 Hz)
= 2.47962 x 10^-13 J

E = hc/λ
λ= hc/E
= (6.63 x 10^-34 js)(3.00 x 10^8 m/s) / (2.47962 x 10^-13 J)
= 8.02139037 x 10^-13 m

x-rays are electromagnetic radiation. So, the easiest way to get back and forth between λ and f is to use the basic wave relation c = λf. Thus, λ = c/f. You can check that this will give the same result for λ_i.

Δλ = λf - λi
λf = Δλ + λi
= ((6.63 x 10^-34 Js) / (9.11 x 10^-31 kg)(3.00 x 10^8 m/s))(1- cos48) + 8.02139037 x 10^-13 m
=4.78097437 x 10^-12 m

Looks set up correctly, but I don't get the same value for λ_f.

Ef = hc/λ
=(6.63 x 10^-34 Js)(3.00 x 10^8 m/s) / (4.78097437 x 10^-12 m)
=4.16023983 x 10^-14 J

E = hf
f = E/h
= (4.16023983 x 10^-14 J) / (6.63 x 10^-34 Js)
= 6.274871536 x 10^-19 Hz

Again, you can just use f = c/λ.

 

[Kennedy111]

Wait... was your λf value 1.06771397 x 10^-12 ??

My calculator was in radian mode...

 

[TSny]

Wait... was your λf value 1.06771397 x 10^-12 ??

My calculator was in radian mode...

I get about 1.605 x 10^-12 m

 

[Kennedy111]

Hmm... I'm not sure what I'm doing wrong then...

 

[Kennedy111]

Nevermind! I got it now! :D Thanks :)