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JEE Main 20206 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
6 September
Shift
Evening Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2020 · 6 September · Evening Shift · Physics · Kinetic Theory of Gases

Assuming the nitrogen molecule is moving with r . m . s . velocity...

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)

Options

  1. A0.24A∘0 . 24\overset{∘}{A}
  2. B0.20A∘0 . 20\overset{∘}{A}
  3. C0.34A∘0 . 34\overset{∘}{A}
  4. D0.44A∘0 . 44\overset{∘}{A}

Correct answer

A. 0.24A∘0 . 24\overset{∘}{A}

Step-by-step solution

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 . 24\overset{°}{A}

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