A beam of neutrons, each moving with speed 2.0×10³ m·s⁻¹, is incident on a crystal with interplanar spacing 0.20 nm. Take neutron mass mₙ = 1.67×10⁻²⁷ kg and h = 6.63×10⁻³⁴ J·s. If first-order Bragg diffraction occurs at angle 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

A beam of neutrons, each moving with speed 2.0×10³ m·s⁻¹, is incident on a crystal with interplanar spacing 0.20 nm. Take neutron mass mₙ = 1.67×10⁻²⁷ kg and h = 6.63×10⁻³⁴ J·s. If first-order Bragg diffraction occurs at angle 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

First calculate the neutron de Broglie wavelength: λ = h ÷ (mₙv). Substitute: λ = 6.63×10⁻³⁴ ÷ [1.67×10⁻²⁷×2.0×10³] ≈ 1.99×10⁻¹⁰ m = 0.199 nm. For first-order Bragg diffraction, 2d sinθ = λ. Thus, sinθ = 0.199 ÷ [2×0.20] = 0.199 ÷ 0.40 ≈ 0.498. Therefore, θ ≈ 29.9°. To the nearest integer, N = 30.