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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)

Photon

=> E2 / E1 = h c / λ * 2 λ² m / h²

====================

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

================

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

=>

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

**=> λ = h c /E2***E2 = h ν = h c /λ*=> E2 / E1 = h c / λ * 2 λ² m / h²

*= 2 m c λ / h*====================

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

================

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*