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JEE Main 20198 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
8 April
Shift
Evening Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2019 · 8 April · Evening Shift · Physics · Kinetic Theory of Gases

The temperature, at which the root mean square velocity of hydrogen...

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape their escape velocity from the earth, is closest to:
[[ Boltzmann Constant kB=1.38×10−23J/K{k}_{B} = 1.38 \times {10}^{- 23}J / K
Avogadro number NA=6.02×1026/kg{N}_{A} = 6.02 \times {10}^{26} / kg
Radius of Earth: 6.4×106m6.4 \times {10}^{6}m
Gravitational acceleration on Earth =10ms−2]= 10m{s}^{- 2} ]

Options

  1. A3×105K3 \times {10}^{5}K
  2. B650K650K
  3. C800K800K
  4. D104K{10}^{4}K

Correct answer

D. 104K{10}^{4}K

Step-by-step solution

3RTm=11.2km/s\sqrt{\dfrac{3RT}{m}} = 11 . 2km / s
3×253×T2×10−3=(11.2×103)2\dfrac{3 \times \dfrac{25}{3} \times T}{2 \times {10}^{- 3}} = {\left(11 . 2 \times {10}^{3}\right)}^{2}
T=10035.2K≈104KT = 10035 . 2K \approx {10}^{4}K
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