At what temperature will the rms speed of oxygen molecule will be sufficient for escaping from the earth?
$(v_{e} = 11.2 k m s^{- 1}, m a s s o f o x y g e n m o l e c u l e = 2.76 \times 10^{- 26} k g a n d k = 1.38 \times 10^{- 23} J k^{- 1})$

Question

At what temperature will the rms speed of oxygen molecule will be sufficient for escaping from the earth?

$(v_{e} = 11.2 k m s^{- 1}, m a s s o f o x y g e n m o l e c u l e = 2.76 \times 10^{- 26} k g a n d k = 1.38 \times 10^{- 23} J k^{- 1})$

Infinity Learn · Accepted Answer

Let the temperature be T.According to kinetic theory of gases, translational  $$KE$$$$=32kTThe$$ oxygen molecule will escape from earth if,  $$32kT$$>$$12mve2i$$.e.,  T>$$mve23k$$  or  T>$$2.76$$×$$10$$−$$26$$×$$(11.2$$×$$103)23$$×$$1.38$$×$$10$$−$$23T$$>$$8.36$$×$$104K$$.

At what temperature will the rms speed of oxygen molecule will be sufficient for escaping from the earth?
$(v_{e} = 11.2 k m s^{- 1}, m a s s o f o x y g e n m o l e c u l e = 2.76 \times 10^{- 26} k g a n d k = 1.38 \times 10^{- 23} J k^{- 1})$

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At what temperature will the rms speed of oxygen molecule will be sufficient for escaping from the earth? ve=11.2 km s−1, mass of oxygen molecule=2.76×10−26 kg and k=1.38×10−23J k−1

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At what temperature will the rms speed of oxygen molecule will be sufficient for escaping from the earth?
$(v_{e} = 11.2 k m s^{- 1}, m a s s o f o x y g e n m o l e c u l e = 2.76 \times 10^{- 26} k g a n d k = 1.38 \times 10^{- 23} J k^{- 1})$