CH 39 #16 - 39.16 The condition for a maximum is h h mh d...

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Unformatted text preview: 39.16: The condition for a maximum is h h mh d sin θ = mλ. λ = = , so θ = arcsin . (Careful! Here, m is the order of the p Mv dMv maximum, whereas M is the incoming particle mass.) h    a)  m = 1 ⇒ θ1 = arcsin dMv 6.63 × 10 −34 J ⋅ s = arcsin (1.60 × 10 −6 m) (9.11 × 10 −31 kg) (1.26 × 10 4 m s) = 2.07°. ( 2) (6.63 × 10 −34 J ⋅ s) m = 2 ⇒ θ 2 = arcsin −6 −31 4 (1.60 × 10 m) (9.11 × 10 kg) (1.26 × 10 m s) = 4.14°.    b) For small angles (in radians!) y ≅ Dθ , so π radians y1 ≈ (50.0 cm) (2.07°) = 1.81 cm. 180° π radians y 2 ≈ (50.0 cm) (4.14°) = 3.61 cm 180° ⇒ y 2 − y1 = 3.61 cm − 1.81 cm = 1.81 cm. ...
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