Finding initial wavelength of photo given angle of deflection

[negation]

Homework Statement

Find the initial wavelength of a photon that loses half its energy when it Compton-scatters from an electron and emerges at 90∘ to its initial direction of motion.

The Attempt at a Solution

E_i = E_f +KE
E_i = 0.5E_i + KE

Using compton's formula for scattering of photon:

Δλ = λ_f - λ_i = 2.42444x10^-12 m

λ_i = λ_f - 2.42444x10^-12 m

pretty much stuck. If I know the initia energy, find the initial wavelength would be a breeze but I don't have that information. Or if I know the numerical value of KE, I can by KE = 0.5E_i, find initial wavelength.

 

[BvU]

What did you do with the 90 degrees information ?

[edit] Oops, already used. Good. So what does halving the energy do to the wavelength of a photon ?

 

[negation]

What did you do with the 90 degrees information ?

[edit] Oops, already used. Good. So what does halving the energy do to the wavelength of a photon ?

not really sure if I will incur the wrath of the moderators but I already solved it.

The key was introducing E=mc² and E = hf
one learnts that f could be found.
f is also equals to c/λ and with this λ could be found.

 

[BvU]

Well done. No reasons for our good moderating spirits to get excited at all !

 

[HalfLostAndSearching]

But I don't have that either.

I understand your frustration with not having enough information to solve this problem. In order to find the initial wavelength of the photon, we need to know the initial energy of the photon before it Compton-scattered. Without this information, it is not possible to accurately determine the initial wavelength.

One possible solution would be to make an assumption about the initial energy of the photon based on similar scenarios or experimental data. However, this would introduce some level of uncertainty in our calculation.

Another approach could be to use the given information about the angle of deflection to calculate the energy of the photon after scattering, and then use this energy to determine the initial wavelength. This would require knowledge of the electron's mass and the angle of deflection, and would also introduce some level of uncertainty.

In summary, without knowing the initial energy of the photon, it is not possible to accurately determine the initial wavelength. Further information or assumptions would be needed to solve this problem.