QJEEM19Ph04e0: JEE Main 2019 Physics - Class 11 JEEM19Ph04e0 Solution: The temperature, at which the root mean square velocity of…

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QJEEM19Ph04e0: JEE Main 2019 Physics - Class 11 JEEM19Ph04e0 Solution: The temperature, at which the root mean square velocity of…

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth, is closest to :
[Boltzmann Constant k_B = 1.38 × 10^–23 J/K Avogadro Number N_A = 6.02 × 10²⁶ /kg Radius of Earth : 6.4 × 10⁶ m Gravitational acceleration on Earth = 10ms^–2]

Multiple Choice Options

A 3 × 105 K
B 104 K
C 650 K
D 800 K

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Accepted Answer

V_{r m s} = \sqrt{\frac{3 R T}{M}} = 11.2 \times 10^{3} m / s

\Rightarrow

T = \frac{M}{3 R} \times {(11.2 \times 10^{3})}^{2}

=

\frac{2 \times 10^{- 3}}{3 \times 8.3} \times 125.44 \times 10^{6} = 10^{4} K

QJEEM19Ph04e0: JEE Main 2019 Physics - Class 11 JEEM19Ph04e0 Solution: The temperature, at which the root mean square velocity of…

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