Neutrons in thermal equilibrium with matter at 27° C can be thought to behave like an ideal gas. Assuming them to have a speed of v text rms , their de-Broglie wavelength is λ (in nm). Find ((156/11)) λ. (Take mn=1.69 × 10-27 kg, .k=1.44 × 10-23 J / K , h=6.60 × 10-34 Js )

Question

Neutrons in thermal equilibrium with matter at 27° C can be thought to behave like an ideal gas. Assuming them to have a speed of v text rms , their de-Broglie wavelength is λ (in nm). Find ((156/11)) λ. (Take mn=1.69 × 10-27 kg, .k=1.44 × 10-23 J / K , h=6.60 × 10-34 Js ) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

v rms =√(3 k T/mn) ; λ=(h/p) ⇒ λ=(h/mn × v rms )=(h/√3 k T mn) ⇒ λ=(6.6 × 10-34/√3 × 1.44 × 10-23 × 1.69 × 10-27 × 300) =(2.2 × 10-10/1.2 × 1.3) ⇒ (156/11) ⋅ λ=(156 × 2.2 × 10-10/11 × 1.2 × 1.3) =(220 × 10-10/11) =(22/11) nm =2 nm

Q. Neutrons in thermal equilibrium with matter at 27∘C can be thought to behave like an ideal gas. Assuming them to have a speed of vrms ​, their de-Broglie wavelength is λ (in nm). Find (11156​)λ. (Take mn​=1.69×10−27kg,k=1.44×10−23J/K,h=6.60×10−34Js)

vrms​=mn​3kT​​;λ=ph​ ⇒λ=mn​×vrms​h​=3kTmn​​h​ ⇒λ=3×1.44×10−23×1.69×10−27×300​6.6×10−34​ =1.2×1.32.2×10−10​ ⇒11156​⋅λ=11×1.2×1.3156×2.2×10−10​ =11220×10−10​ =1122​nm=2nm