hw28 - Physics 21 Fall 2004 Solution to HW-28 38 P 31...

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Physics 21 Fall, 2004 Solution to HW-28 38 P31 Calculate the wavelength of a 0.21 kg ball traveling at 0.1 m/s. λ = h p = h mv = 6 . 63 × 10 - 34 0 . 21 × 0 . 1 =3 . 2 × 10 - 32 m 38 P32 What is the wavelength of a neutron ( m =1 . 67 × 10 - 27 kg) traveling at 5 . 5 × 10 4 m/s? λ = h p = 6 . 63 × 10 - 34 (1 . 67 × 10 - 27 )(5 . 5 × 10 4 ) =7 . 2 × 10 - 12 m 38 P36 Show that if an electron and a proton have the same nonrelativistic kinetic energy, the proton has the shorter wavelength. Use the nonrelativistic relation between kinetic energy E , momentum p , and mass m : E = p 2 2 m p = 2 mE. Then λ = h p = h 2 mE For equal energies E , the larger mass of the proton will lead to a smaller de Broglie wavelength. 39 P3 A proton is traveling with a speed of (4 . 825 ± 0 . 012) × 10 5 m/s. With what maximum accuracy can its position be ascertained? The value of ∆ p is the range of likely values of p ,and p = m v . We take ∆ v =0 . 024 × 10 5 m/s (the full range
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