How to derive characteristic wavelength of x-ray from energy equation?

[boladore]

Hello. first, sorry for my poor English.
Derive characteristic wavelength from radiation powerThis is radiated power from bending magnet (synchrotron storage ring accelerating electron to get x-ray)

and these are wave distribution from storage ring

and what I have to derive is as follows. characteristic wavelength of radiation

I have to derive this equation. professor said I can derive this equation from the first power equation. I have been trying for 3 days. but couldn't find solution.
help...

Best regards.

 

[member 553083]

The characteristic wavelength of radiation is related to the power, which is given by the equation:λ_c = (hc/P)^1/2where h is Planck's constant, c is the speed of light and P is the power of the radiation.To derive this equation from the power equation you first need to calculate the energy of the radiation, E, which is given by the equation:E = P/fwhere f is the frequency of the radiation.Then using the equation for the energy of a photon, which is given by:E = hfyou can solve for the frequency, f, which is given by:f = E/hThen using the equation for the wavelength of a photon, which is given by:λ = c/fyou can solve for the wavelength, λ, which is given by:λ = c/(E/h)Finally, substituting the equation for the energy of the radiation, E = P/f, gives the equation for the characteristic wavelength of the radiation:λ_c = (hc/P)^1/2