1.

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

Answer»

nck's constant,         p = momentum of electron,        m = mass of electron V = velocity of electron,          ν = frequency of wave of photonλ = wavelength of photon        E1 = kinetic energy of electronE2 = Kinetic energy of photon        c = speed of lightDeBroglie 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         ====================for exampleenergy 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 electronsubstitute 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



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