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

Question

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

Tardigrade Admin · Accepted Answer

vr m s=√(3 k T/m) ; λ=(h/p) ⇒ λ=(h/mn × vr m s)=(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)=(11 × 2 × 10-9/156) =(11 × 2/156) nm

Q. Neutrons in thermal equilibrium with matter at 27∘C can be thought to behave like ideal gas. Assuming them to have a speed of vrms ​, If the de-Broglie wavelength λ is (15611N​)nm. The value of N is______. [Take mn​=1.69×10−27kg,k=1.44×10−23J/K,h=6.60×10−34Jsec]

vrms​=m3kT​​;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​=15611×2×10−9​ =15611×2​nm