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At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Given : Mass of oxygen molecule $(m) = 2.76 \times 10^{- 26} kg, Boltzmann's constant k_{B} = 1.38 \times 10^{- 23} {JK}^{- 1})$

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2.508×104 K

8.360×104 K

5.016×104 K

1.254×104 K

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detailed solution

Correct option is B

Escape velocity from the Earth's surface is vescape =11200 m s-1Say at temperature T, oxygen molecule attains escape velocity. So, vescape =3kBTmO2⇒11200=3×1.38×10-23×T2.76×10-26 On solving, T=8.360×104 K

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At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Given : Mass of oxygen molecule (m)=2.76×10-26 kg, Boltzmann's constant kB=1.38×10-23JK-1

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Ready to Test Your Skills?

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At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Given : Mass of oxygen molecule $(m) = 2.76 \times 10^{- 26} kg, Boltzmann's constant k_{B} = 1.38 \times 10^{- 23} {JK}^{- 1})$