An electron beam is produced by accelerating electrons from rest through an unknown potential difference. The beam produces a first-order Bragg diffraction maximum from crystal planes of spacing 1.50 Å at a Bragg angle of 30°. Use 2d sinθ = λ and λ(Å) = 12.27 ÷ √V. If the accelerating potential is approximately N V, find N to the nearest integer.
Physics · Photoelectric effect and dual nature of matter · debroglie duel nature of light
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Question

An electron beam is produced by accelerating electrons from rest through an unknown potential difference. The beam produces a first-order Bragg diffraction maximum from crystal planes of spacing 1.50 Å at a Bragg angle of 30°. Use 2d sinθ = λ and λ(Å) = 12.27 ÷ √V. If the accelerating potential is approximately N V, find N to the nearest integer.

Physics · Photoelectric effect and dual nature of matter · debroglie duel nature of light

G1 Physics · Accepted Answer

First use Bragg's law: λ = 2d sinθ. Substitute d = 1.50 Å and θ = 30°: λ = 2×1.50×0.5 = 1.50 Å. Now use the electron wavelength relation: 1.50 = 12.27 ÷ √V. Therefore, √V = 12.27 ÷ 1.50 = 8.18. Hence, V = 8.18² ≈ 66.9 V. To the nearest integer, N = 67.