Ai 8 1012 v phase 10 4 m s 8 k 8 10

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Unformatted text preview: nergy is now ΔE = 9.1 × 10 −31 0.65 = 27.8 meV 5 × 10 −28 2.22 (a) An electron in free space is described by a plane wave given by Ψ ( x, t ) = Aei ( kx−ω t ) . If k = 8 x 108 /m, and ω is 8 x 1012 rad/s, determine the (i) phase velocity and wavelength of the plane wave, and the (ii) momentum and kinetic energy (in eV) of the electron. (b) Repeat part (a) for k = - 1.5 x 109 /m and ω of 1.5 x 1013 rad/s. (a)(i) ω 8 × 1012 v phase = = = 10 4 m / s 8 k 8 × 10 2π 2π λ= = = 7.85 nm k 8 × 10 8 (ii) p = k = 1.05459 × 10 −34 ⋅ 8 × 10 8 = 8.44 × 10 −26 kg ⋅ m / s p2 (8.44 × 10 −26 )2 E= = = 24.5 meV 2 m 2 ⋅ 9.1 × 10 −31 ⋅ 1.6 × 10 −19 (b)(i) ω 1.5 × 1013 v phase = = − = −10 4 m / s k 1.5 × 10 9 2π 2...
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This document was uploaded on 02/19/2014.

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