Question

what is the ratio of kinetic energy of photon to electron with the same wavelength ?

Answer 1

h = Planck's constant,         p = momentum of electron,        m = mass of electron
v = velocity of electron,          ν = frequency of wave of photon
λ = wavelength of photon        E1 = kinetic energy of electron
E2 = Kinetic energy of photon        c = speed of light

DeBroglie wavelength of electron = λ = h / p
     p = m v  =>    p²  =  2 m E1      =>  p = √(2 m E1)        =>  λ = h /√(2 m E1)
              E1 = h² / (2 λ² m)

Photon
     E2 = h ν = h c /λ            =>        λ = h c /E2

    => E2 / E1 = h c / λ  * 2 λ² m / h²
                     = 2 m c λ / h        
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for example
energy of photon to energy of electron with the same wavelength 500 nm
              =  2 * 9.11 * 10⁻³¹ * 3 * 10⁸ * 500 * 10⁻⁹ / 6.636 * 10⁻³⁴
             = 0.008237
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wavelength of electron :  λ = h / p  = h / m v,        v = velocity of electron

substitute this value in the ratio of energies.

   E2 / E1 = 2 m c λ / h = 2 m c (h / m v) /  h
   =>  E2 / E1  = 2 c / v