Verified Solution • 2025–26 Session moderate

QJEEM22Phb493: JEE Main 2022 Physics - Class 11 JEEM22Phb493 Solution: The root mean square speed of smoke particles of mass in their…

The root mean square speed of smoke particles of mass 5×10−17 kg5 \times 10^{-17} \mathrm{~kg} in their Brownian motion in air at NTP is approximately. [Given k=1.38×10−23JK−1\mathrm{k}=1.38 \times 10^{-23} \mathrm{JK}^{-1} ]

Multiple Choice Options

  • A 60 mm s−160 \mathrm{~mm} \mathrm{~s}^{-1}
  • B 12 mm s−112 \mathrm{~mm} \mathrm{~s}^{-1}
  • C 15 mm s−115 \mathrm{~mm} \mathrm{~s}^{-1}
  • D 36 mm s−136 \mathrm{~mm} \mathrm{~s}^{-1}

Step-by-Step Verified Solution

At NTP, T=298 KT=298 \mathrm{~K}

vrmsamp;=3RTMamp;=3kNA×2985×10−17×NA\begin{aligned}v_{\mathrm{rms}} &=\sqrt{\frac{3 R T}{M}} \\&=\sqrt{\frac{3 k N_{A} \times 298}{5 \times 10^{-17} \times N_{A}}}\end{aligned}

≃15 mm/s\simeq 15 \mathrm{~mm} / \mathrm{s}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring