Hwksolns8_Publishers

Hwksolns8_Publishers - Publisher's Solution for HW 8...

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Unformatted text preview: Publisher's Solution for HW # 8 CONCEPTUAL QUESTIONS 25.1. 1 θ decreases. As the crystal is compressed, the spacing d between the planes of atoms decreases. The Bragg condition is 2 cos m m d λ θ = so as d decreases, cos m θ must increase. But cos θ increases as θ decreases. 25.2.(a) a b c E E E because the energy per photon depends only on the frequency so / . E hf hc λ = = The smaller wavelengths correspond to higher frequencies. (b) c b a N N N because the powers are equal, there must be more photons when the energy per photon is less. 25.3. 2 2 1 1 1 1 / 1 / 2 2 E hc E hc λ λ λ λ = = = 25.5. Fast electrons will have a shorter wavelength leading to less diffraction spreading and better resolution. 25.7. Because 2 2 2 8 n h E n mL = we see that for a given n , n E is inversely proportional to 2 L . If L is doubled then n E is decreased by a factor of 4. So the new 19 1 1 10 J. E- = × 25.8. It is the same, or 20 1.0 10 J.- × 1 1 1 2 2 H He H 2 2 8 8(4 ) 2 h h E E E m L L m = = = EXERCISES AND PROBLEMS 25.4.Model: The angles of incidence for which diffraction from parallel planes occurs satisfy the Bragg condition. Solve: The Bragg condition is 2 cos , m d m θ λ = where m = 1, 2, 3, … For first and second order diffraction, ( 29 1 2 cos 1 d θ λ = , ( 29 2 2 cos 2 d θ λ = Dividing these two equations, ( 29 ( 29 1 1 2 2 1 1 cos 2 cos 2cos cos 2cos68 41 cos θ θ θ θ-- = ⇒ = = ° = ° 25.7.Model: The angles corresponding to the various diffraction orders satisfy the Bragg condition. Solve: The Bragg condition is 2 cos m d m θ λ = , where m = 1, 2, 3, … The maximum possible value of m is the number of possible diffraction orders. The maximum value of cos θ m is 1. Thus, ( 29 ( 29 2 0.180 nm 2 2 4.2 0.085 nm d d m m λ λ = ⇒ = = = We can observe up to the fourth diffraction order....
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Hwksolns8_Publishers - Publisher's Solution for HW 8...

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