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JEE Main 201815 AprilEvening ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Evening Shift
Mode
Online
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2018 · 15 April · Evening Shift · Online · Physics · Kinetic Theory of Gases

The value closest to the thermal velocity of a Helium atom at room...

The value closest to the thermal velocity of a Helium atom at room temperature (300 K)(300 \mathrm{~K}) in ms−1\mathrm{ms}^{-1} is: [kB=1.4×10−23 J/K;mHe=7×10−27 kg]\left[\mathrm{k}_{\mathrm{B}}=1.4 \times 10^{-23} \mathrm{~J} / \mathrm{K} ; \mathrm{m}_{\mathrm{He}}=7 \times 10^{-27} \mathrm{~kg}\right]

Options

  1. A1.3×1041.3 \times 10^4
  2. B1.3×1051.3 \times 10^5
  3. C1.3×1021.3 \times 10^2
  4. D1.3×1031.3 \times 10^3

Correct answer

D. 1.3×1031.3 \times 10^3

Step-by-step solution

v=3kBT/mHe=3×1.4×10−23×3007×10−27=1.34×103 m/s\begin{aligned}v &=\sqrt{3 k_{\mathrm{B}} T / m_{\mathrm{He}}}=\sqrt{\frac{3 \times 1.4 \times 10^{-23} \times 300}{7 \times 10^{-27}}}\\ &=1.34 \times10^3 \mathrm{~m}/ \mathrm{s} \end{aligned}
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