Homework%2003

Homework%2003 - . 10 86 . 7 / 10 52 . 3 10 5 . 1 10 27 . 5...

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EEE 539—Spring 2008 Homework 3 O.K. I only got a 40/50 on this set! 2.11 When the uncertainty principle is considered, it is not possible to locate a photon in space more precisely than about 1 wavelength. Consider a photon with wavelength λ = 1 µ m. What is the uncertainty in the photon’s (a) momentum and (b) energy? (a) 29 6 34 10 27 . 5 10 2 10 05459 . 1 2 2 × = × = = = h h x p kg-m/s. (b) eV J hc hf E 24 . 1 10 2 10 10 3 10 626 . 6 19 6 8 34 = × = × × = = = 2.12 The uncertainty in position is 1.2 nm for a particle of mass 5 × 10 -29 kg. Determine the minimum uncertainty in (a) the momentum of the particle, and (b) the kinetic energy of the particle. (a) 26 9 34 10 4 . 4 10 2 . 1 2 10 05459 . 1 2 × = × × = = x p h kg-m/s. (b) Since we don’t know the momentum of the particle, we have to make the simple assumption that . 120 10 94 . 1 10 5 2 ) 10 4 . 4 ( 2 ) ( ~ 23 29 2 26 2 eV J m p E = × = × × = 2.14 An automobile has a mass of 1500 kg. What is the uncertainty in the velocity (in miles per hour) when its center of mass is located with an uncertainty of no greater than 1 cm?
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Unformatted text preview: . 10 86 . 7 / 10 52 . 3 10 5 . 1 10 27 . 5 / 10 27 . 5 10 2 10 05459 . 1 2 36 36 3 33 33 2 34 mph s m m p v s m kg x p = = = = = = = h 2.17 Consider the wave function t i e x A t x = ) sin( ) , ( for -1 x 1. Determine A so that . 1 ) , ( 1 1 2 = dx t x [ ] . , 1 2 2 ) 2 sin( 2 1 2 2 ) 2 cos( 1 ) ( sin 1 2 2 1 1 2 1 1 2 1 1 2 2 i A A A x x A dx x A dx x A = = = = = = 2.18 Consider the wave function t i e x n A t x = ) sin( ) , ( for 0 x 1. Determine A so that . 1 ) , ( 1 2 = dx t x [ ] . 2 , 2 1 2 ) 2 sin( 2 1 2 2 ) 2 cos( 1 ) ( sin 1 2 2 1 2 1 2 1 2 2 i A A A x n n x A dx x n A dx x n A = = = = = =...
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Homework%2003 - . 10 86 . 7 / 10 52 . 3 10 5 . 1 10 27 . 5...

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