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An electron beam is accelerated by a fixed voltage of V = 6,500.V (V= 6.50 kV). The resolution that this beam can probe depends on the de Broglie wavelength of the electrons. What is the de Broglie wavelength of the electrons, 1 ? What is the energy per photon (in eV) for a beam of X-rays to have the same wavelength, 1 as found in part 'a.' ? a. b.

An electron beam is accelerated by a fixed voltage of V = 6,500.V (V= 6.50 kV). The resolution that this beam can probe depends on the de Broglie wavelength of the electrons. What is the de Broglie wavelength of the electrons, 1 ? What is the energy per photon (in eV) for a beam of X-rays to have the same wavelength, 1 as found in part 'a.' ? a. b.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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10. An electron beam is accelerated by a fixed voltage of V = 6,500.V (V = 6.50 kV ). The resolution that this beam can probe depends on the de Broglie wavelength of the electrons. What is the de Broglie wavelength of the electrons, 1 ? What is the energy per photon (in eV) for a beam of X-rays to have the same wavelength, 1 as found in part 'a.' ? а. b.
Transcribed Image Text:10. An electron beam is accelerated by a fixed voltage of V = 6,500.V (V = 6.50 kV ). The resolution that this beam can probe depends on the de Broglie wavelength of the electrons. What is the de Broglie wavelength of the electrons, 1 ? What is the energy per photon (in eV) for a beam of X-rays to have the same wavelength, 1 as found in part 'a.' ? а. b.
Waves in general: FORMULA PAGE 1 a y 1-dimensional wave equation: 1 a'y ; here v is the speed of the wave v? ôt? Solution: f(x- vt) or f(x+vt) Harmonic or sinusoidal waves: y(x,t)= Asin(kx- ot) 2л k 2n = 27f; v=- T v = f2 General Constants: -34 h = 6.626×10*J.s = 4.13567×10¬eV ·s ; (with recent revisions to the SI system of units Planck's Constant is defined to have an exact value: h= 6.62607015×10¯“J·s) –34 -19 hc = 1240 eV · nm; hc=1239.84eV · nm (for more accuracy); leV =1.6022×10-J = 299,792, 458 m /s (exact); -31 electron mass: m, =9.1094×10' kg proton mass: m, =1.6726×10-27 kg Photons: E = hf hc ; Protons: m,c² = 938.3MEV , Electrons: m.c² = 511.0keV %3| h = 1.0546x10 34J•s = 6.5821×10-1eV ·s Chapter 36. Diffraction Single slit diffraction: Minima: a sin 0, = ma, m=1,2,3,...where a is the slit width, note: there is a maximum at 0 = 0 sin(a) па Intensity: I(0) = ,, a = -sin(0) m a Circular aperture: First minimum: sin 0 = 1.22- Rayleigh's criterion ( 1 <d ): a =1.22- d Double slit experiment with slit separation d and slit width a: sin a Intensity: I(0) = I„(cos? B)| where B = -sin 0 , a = па -sin O Grating equation (normal incidence): d sin 0 = m order in which the grating is being used, d is the line or groove spacing m = 0,1, 2,3,... (maxima), where m is the
Transcribed Image Text:Waves in general: FORMULA PAGE 1 a y 1-dimensional wave equation: 1 a'y ; here v is the speed of the wave v? ôt? Solution: f(x- vt) or f(x+vt) Harmonic or sinusoidal waves: y(x,t)= Asin(kx- ot) 2л k 2n = 27f; v=- T v = f2 General Constants: -34 h = 6.626×10*J.s = 4.13567×10¬eV ·s ; (with recent revisions to the SI system of units Planck's Constant is defined to have an exact value: h= 6.62607015×10¯“J·s) –34 -19 hc = 1240 eV · nm; hc=1239.84eV · nm (for more accuracy); leV =1.6022×10-J = 299,792, 458 m /s (exact); -31 electron mass: m, =9.1094×10' kg proton mass: m, =1.6726×10-27 kg Photons: E = hf hc ; Protons: m,c² = 938.3MEV , Electrons: m.c² = 511.0keV %3| h = 1.0546x10 34J•s = 6.5821×10-1eV ·s Chapter 36. Diffraction Single slit diffraction: Minima: a sin 0, = ma, m=1,2,3,...where a is the slit width, note: there is a maximum at 0 = 0 sin(a) па Intensity: I(0) = ,, a = -sin(0) m a Circular aperture: First minimum: sin 0 = 1.22- Rayleigh's criterion ( 1 <d ): a =1.22- d Double slit experiment with slit separation d and slit width a: sin a Intensity: I(0) = I„(cos? B)| where B = -sin 0 , a = па -sin O Grating equation (normal incidence): d sin 0 = m order in which the grating is being used, d is the line or groove spacing m = 0,1, 2,3,... (maxima), where m is the
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