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