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 \times 10^{-23}\; J/K

Avagadro Number N_{A}=6.02 \times 10^{26}\; /Kg

Radius of Earth: 6.4 \times 10^{6}\; m

Gravitational acceleration on Earth= 10 ms-2]

  • Option 1)

    800 K

  • Option 2)

    3 \times 10^{5}K

  • Option 3)

    10^{4}K

  • Option 4)

    650 K

Answers (1)

Escape speed of particle from earth surface =11.2 km/s

RMS velocity of H2 = \sqrt{\frac{3RT}{m}}

\sqrt{\frac{3 \times \frac{25}{3} \times T}{2 \times 10^{-3}}}=11.2 \;\; km/s=11.2 \times 10^{3} \; m/s

\frac{25T}{2 \times 10^{-3}}=(11.2)^{2}\times 10^{6}

T=\frac{2 \times 125.44 \times 10^{3}}{25}=10035.2K=10^{4}K


Option 1)

800 K

Option 2)

3 \times 10^{5}K

Option 3)

10^{4}K

Option 4)

650 K

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