Electrons are accelerated from rest through 150 V and then incident on a crystal having interplanar spacing 1.00 Å. Use the non-relativistic electron relation λ(Å) = 12.27 ÷ √V and the first-order Bragg condition 2d sinθ = λ. If the Bragg angle is approximately N degrees, find N to the nearest integer.
Physics · Photoelectric effect and dual nature of matter · debroglie duel nature of light
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Question

Electrons are accelerated from rest through 150 V and then incident on a crystal having interplanar spacing 1.00 Å. Use the non-relativistic electron relation λ(Å) = 12.27 ÷ √V and the first-order Bragg condition 2d sinθ = λ. If the Bragg angle is approximately N degrees, find N to the nearest integer.

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

G1 Physics · Accepted Answer

Electron wavelength: λ = 12.27 ÷ √150 Å ≈ 1.002 Å. For first-order Bragg diffraction, 2d sinθ = λ. With d = 1.00 Å: 2(1.00)sinθ = 1.002. Thus, sinθ = 0.501. Therefore, θ ≈ 30.1°. To the nearest integer, N = 30.