Kinetic Theory

JEE Main level, single correct, medium

53 of 168

Question 53 of 168

Assuming the nitrogen molecule is moving with r.m.sr.m.s. velocity at 400K400K, the de-Broglie wave length of nitrogen molecule is close to : (Given : nitrogen molecule weight : 4.64×10−26kg4.64\times {10}^{-26} kg, Boltzman constant : 1.38×10−23JK−11.38\times {10}^{-23} J{K}^{-1}, Planck constant : 6.63×10−34Js6.63\times {10}^{-34} Js)

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Answer: (A) 0.24A∘0.24 A^{^{\circ}}

λ=h2mk=hm×32kT=h3mkT\lambda =\dfrac{h}{\sqrt{2mk}}=\dfrac{h}{\sqrt{m\times \dfrac{3}{2}kT}}=\dfrac{h}{\sqrt{3mkT}}
=6.63×10−343×4.64×10−26×1.38×10−13×400=0.24A∘=\dfrac{6.63\times {10}^{-34}}{\sqrt{3\times 4.64\times {10}^{-26}\times 1.38\times {10}^{-13}\times 400}}=0.24A^{^{\circ}}

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