PLZ SHOW WORKING FOR THE SOLUTION, THANKS! Let us understand why the moon has no

Question

PLZ SHOW WORKING FOR THE SOLUTION, THANKS!

Let us understand why the moon has no atmosphere......We need to remember some mechanics here! Taking the temperature of the surface of the moon to be 107 degree C (actually this is the mean day-time temperature), calculate the root mean square speed of oxygen gas molecules in any putative atmosphere. What is their mean translational kinetic energy? What is their potential energy at the moon's surface? What is the escape velocity? Why does the moon have no atmosphere (and why does the earth have one)? [Radius of moon = 1738 km. Acceleration due to gravity on moon = 1.62 ms-2].

Explanation / Answer

a) 1/2 mv^2 = 5/2 k T 0.5*5.31E-26*v^2 = 2.5*1.38E-23*(107+273) v=702.7 m/s b) KE =1/2 mv^2=0.5*5.31E-26*(702.7)^2=1.31E-20 J c) PE = - G M m/R = - (G M/R^2) m R = - m g R = -5.31E-26*1.62*1738E3=-1.495E-19 J d) KE is when v=0 r-> infinity 1/2 mv^2 - G M m/R = 0 0.5*v^2 - g R = 0 v=sqrt(2*9.81*1738E3)=5839 m/s e) here the velocity of the gas is s sizable fraction of the escape velocity so it can sometimes escape. on earth it can't

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