PC Chapter 05

PC Chapter 05 - 5 Matter Waves 5-1 = h h 6.63 10 34 Js = =...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
67 5 Matter Waves 5-1 ( 29 λ - - - × = == × 34 6 13 27 6.63 10 Js 10 m s 3.97 10 m 1.67 10 kg hh p mv 5-2 The issue is: Can we use the simpler classical expression (29 = 12 2 p mK instead of the exact relativistic expression ( 29 + = 2 2 1 mc K K p c ? As the relativistic expression reduces to = 2 p mK for << 2 2 K mc , we can use the classical expression whenever << 1 MeV K because 2 mc for the electron is 0.511 MeV. (a) Here << 50 eV 1 MeV , so = 2 p mK ( 29( 29( [ ] ( λ =   × 2 0.511 MeV 6 2 2 0.511 MeV 50 eV 2 50 eV 1 240 eV nm 0.173 nm 2 0.511 10 50 eV c h h hc p (b) As << 50 eV 1 MeV , = 2 p mK ( λ - = × 2 3 3 0.511 MeV 5.49 10 nm 2 50 10 eV c hc . As this is clearly a worse approximation than in (a) to be on the safe side use the relativistic expression for p : + = 2 2 1 mc K pK c so ( ( ( λ - = + × + ×× = ×= 2 22 3 36 3 1 240 eV nm 2 50 10 2 50 10 0.511 10 eV 5.36 10 nm 0.005 36 nm h hc p K Kmc
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
68 CHAPTER 5 MATTER WAVES 5-3 ( 29 λ - - × = == 34 36 6.63 10 Js 5 m s 1.79 10 m 74 kg hh p mv 5-4 Taking λ= 0.1 nm and using λ h p mv , we get ( λ - - - × × × 34 96 31 6.63 10 Js 0.1 10 m 7.28 10 m s 9.11 10 kg h v m . As << vc , it is okay to use = p mv instead of γ = p mv . 5-5 (a) λ = h p or ( (29 λλ = = 1 240 eV nm 124 eV 10 nm h hc p c cc . As ( 29  = - = +-  12 2 2 2 2 22 K E mc p c mc mc , we must use the relativistic expression for K , when 2 pc mc . Here = < <= 2 124 eV 0.511 MeV pc mc , so we can use the classical expression for K , = 2 2 p K m . = = 2 2 2 124 eV 0.150 eV 2 2 0.511 MeV 2 p pc K m mc (b) Electrons with λ λ = 12 400 eV 0.10 nm hc p as in (a). As < 2 0.511 MeV pc mc , use ( ( = = × 2 2 2 6 12 400 eV 150 eV 2 2 0.511 10 eV p K m . (c) Electrons with λ - = 15 10 fm 10 10 m , λ × 3 1.24 10 MeV hc p . As = 2 0.511 MeV pc mc , use = + - = - =-= 2 2 2 2 1 240 MeV 0.511 MeV 1 239 MeV K p c mc mc pc mc . For alphas with = 2 3 726 MeV mc : (a) p still is 124 eV c . As << 3 726 MeV pc , we use = 2 2 p K m : ( - = = 2 6 2 124 eV 2.06 10 eV 2 3 726 MeV 2 K mc .
Background image of page 2
MODERN PHYSICS 69 (b) For alphas with λ= 0.10 nm , = 12 400 eV p c . As < <= 2 3 726 MeV pc mc , ( 29 (29 ( = = == 2 2 22 2 12 400 eV 0.020 6 eV 2 2 3 726 MeV 2 p pc K m mc . (c) × = 3 1.24 10 MeV p c and 2 1 240 MeV~ 3 726 MeV pc mc . We use ( 29 ( (  = + - = +-  = 12 2 2 2 1 240 MeV 3 726 MeV 3 726 MeV 201 MeV. K p c mc mc 5-6 From Problem 5-2, a 50 keV electron has λ - 3 5.36 10 nm . A 50 keV proton has = < 2 50 keV 2 1 877 MeV K mc so we use = 2 p mK : ( ( ( [ ] ( ( λ - = = ×× 2 938.3 MeV 4 33 2 938.3 MeV 50 keV 2 50 keV 1 240 eV nm 1.28 10 nm 2 938.3 10 eV 50 10 eV c h h hc p 5-7 A 10 MeV proton has = < 2 10 MeV 2 1 877 MeV K mc so we can use the classical expression = 2 p mK . (See Problem 5-2) ( 29( 29( [ ] λ - = = = = 15 2 1 240 MeV fm 9.05 fm 9.05 10 m 2 938.3 MeV 10 MeV 2 938.3 10 MeV h hc p 5-8 λ - = =  2 h h hh V p mK meV me ( 29 λ λ - - -- - - × = × = 34 31 19 92 6.626 10 Js 2 9.105 10 kg 1.602 10 C 1.226 10 kg m V V sC 5-9 = 0.20 kg m : = 2 2 mv mgh : = 2 v gh ( 29 ( [ ] λ - - = = = =⋅ ×⋅ = = 34 34 2 0.20 2 9.80 50 6.261 kg m s 6.626 10 J s 1.06 10 m 6.261 kg m s p mv m gh h p
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
70 CHAPTER 5 MATTER WAVES 5-10 As ( 29 λ = == 0 2 2 0.052 9 nm 0.105 8 nm a the energy of the electron is nonrelativistic, so we can use ( ( ( λ λ - - -- ×⋅ = ×= ×× 2 2 34 2 18 22 31 10 with ; 2 6.626 10 J s 21.5 10 J 134 eV 2 2 9.11 10 kg 1.058 10 m p h pK m h K m This is about ten times as large as the ground-state energy of hydrogen, which is 13.6 eV.
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/05/2009 for the course PHSX 313 taught by Professor Staff during the Fall '09 term at Kansas.

Page1 / 14

PC Chapter 05 - 5 Matter Waves 5-1 = h h 6.63 10 34 Js = =...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online