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 !