05459 10 2 2 073nm k 863 10 9 mv 2 91 10 31 10

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Unformatted text preview: λ= = = 4.19 nm k 1.5 × 10 9 (ii) p = k = −1.05459 × 10 −34 ⋅ 1.5 × 10 9 = 1.58 × 10 −25 kg ⋅ m / s p2 (1.58 × 10 −25 )2 E= = = 85.9 meV 2 m 2 ⋅ 9.1 × 10 −31 ⋅ 1.6 × 10 −19 2.24 Determine the wave number, wavelength, angular frequency, and period of a wave function that describes an electron traveling in free space at a velocity of (a) 5 x 106 cm/s and (b) 108 cm/s. (a) k= λ= ω= T= (b) mv 9.1 × 10 −31 ⋅ 5 × 10 4 = = 4.3 × 10 8 / m −34 1.05459 × 10 2π 2π = = 14.6 nm k 4.3 × 10 8 mv 2 9.1 × 10 −31 (5 × 10 4 )2 13 = = 1.08 × 10 rad / s 2 2 ⋅ 1.05459 × 10 −34 2π 2π = = 0.58 ps ω 1.08 × 1013 mv 9.1 × 10 −31 ⋅ 10 6 = = 8.63 × 10 9 / m −34 1.05459 × 10 2π 2π λ= = = 0.73nm k 8.63 × 10 9 mv 2 9.1 × 10 −31 (10 6 )2 15 ω= = = 4.34 × 10 rad / s 2 2...
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