Verified Solution • 2025–26 Session moderate

QJEEM20Ph70ef: JEE Main 2020 Physics - Class 12 JEEM20Ph70ef Solution: Assuming the nitrogen molecule is moving with r.m.s. velocity…

Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wavelength of nitrogen molecule is close to :
(Given : nitrogen molecule weight : 4.64 × 10–26 kg,
Boltzman constant: 1.38 × 10–23 J/K,
Planck constant : 6.63 × 10–34 J.s)

Multiple Choice Options

  • A 0.44 Ao
  • B 0.34 Ao
  • C 0.20 Ao
  • D 0.24 Ao

Step-by-Step Verified Solution

We know, the de-Broglie wavelength

λ = hmvrms

also Vrms = 3kTm

∴ λ = h3mkT

= 6.63×10−343×4.6×10−26×1.38×10−23×400

= 2.4 × 10-11 m

= 0.24 Ao

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