Question

2. The potential energy of two masses, m, and m, separated by a distance r is given by: Gm.my VO) --- G 6.67X10" J m ka? Suppose a particle of mass m has a velocity v perpendicular to the earth's surface. Show that the minimum velocity that the particle must have in order to escape the earths surface 2GM. von Roth Then, considering that Mon = 5.98x1024 kg and Ron = 6.36x10m is its mean radius, calculate the escape velocity of a hydrogen molecule and a nitrogen molecule. What temperature would each of these molecules have to have so that their average speed exceeds their escape velocity?

Answer 1

- It the particle escape than energy it reo should be zero. so wing conservation of energy Env² GmM =0 1 IULUI = And for earth G=11.2km/sec. ve 6.67X16x 5.98X10 = 1/-2 kemisen V 6-36 X 70%m for molescules average velocity is TEERT, TE POM 8R For hydrogen . T= (1 1-2x103) 7ny 2x10 - 11850k ex 8-314 for Nitrogen (11-2x133)x 71 x BX 10 848.314 = 165894K -