PART ONE

If it has enough kinetic energy, a molecule
at the surface of the Earth can escape the Earth’s gravitation.
The acceleration of gravity is 9.8 m/s^2
,and the Boltzmanns’ constant is 1.38066 ×
10^−23 J/K. Using energy conservation, determine the minimum kinetic energy needed to escape in terms of the mass of the molecule m, the
free-fall acceleration at the surface g, and the
radius of the Earth R. (IMAGE)

PART TWO
Calculate the temperature for which the minimum escape energy is 15 times the average
kinetic energy of an oxygen molecule.
Answer in units of K.