# Momentum wavelength relationship for photons i in

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Momentum-wavelength relationship for photons I In classical mechanics, momentum is a conserved “amount of motion” calculated by p = mv I Einstein’s other great contribution, relativity theory, gives the following relationship between energy, momentum, and “rest mass” (ordinary mass, m 0 ): E 2 = c 2 p 2 + m 2 0 c 4 I Photons are massless, so m 0 = 0, which gives E = cp . I Since E is also equal to hc , we get p = h λ

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Example: Calculations of wave/photon properties Fluorescent light contains a strong green line with a wavelength of 546 nm. From the wavelength, we can calculate the following: ν = c λ = 2 . 997 924 58 × 10 8 m / s 546 × 10 - 9 m = 5 . 49 × 10 14 Hz E = h ν = (6 . 626 069 57 × 10 - 34 J / Hz)(5 . 49 × 10 14 Hz) = 3 . 64 × 10 - 19 J p = h λ = 6 . 626 069 57 × 10 - 34 J / Hz 546 × 10 - 9 m = 1 . 21 × 10 - 27 kg m / s E m = N A E = (6 . 022 141 99 × 10 23 mol - 1 )(3 . 64 × 10 - 19 J) = 219 kJ / mol p m = N A p = (6 . 022 141 99 × 10 23 mol - 1 )(1 . 21 × 10 - 27 kg m / s) = 7 . 31 × 10 - 4 kg m s - 1 mol - 1
Some typical numbers Source λ ν E m CKXU 88.3 FM: 3.40 m 88.3 MHz 35.2 mJ/mol Microwave oven: 12.2 cm 2.45 GHz 0.978 J/mol Green light: 546 nm 549 THz 219 kJ/mol Near UV: 300 nm 1 PHz 400 kJ/mol Far UV: 100 nm 3 PHz 1 MJ/mol Medical diagnostic X-rays: 31 pm 10 EHz 4 GJ/mol
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• Fall '06
• Marc

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