If it has enough kinetic energy, a moleculeat the surface of the Earth can escap

Question

If it has enough kinetic energy, a moleculeat the surface of the Earth can escape the Earth’s gravitation.The acceleration of gravity is 9.8 m/s2,and the Boltzmanns’ constant is 1.38066×1023 J/K. Using energy conservation, determine theminimum kinetic energy needed to escape interms of the mass of the molecule m , the free-fall acceleration at the surface g, and the radius of the Earth R

b)Calculate the temperature for which the min- imum escape energy is 11 times the average kinetic energy of an oxygen molecule.

some one please help me solve part b step by step

Please only respond if it is correct

Explanation / Answer

b)  the minimum kinetic energy needed to escape=mgR

  the average kinetic energy of an oxygen molecule = (3/2)kT

Now acc. to statement, mgR = 11* (3/2)kT

where m=32g/mole x 1kg/1000g x 1mole/6.022x10^23molecules = 5.3x10^-26kg/molecule

R= 6400 km

5.3x10^-26*9.8*6400000 = 11*1.5* 1.38066×10^23 *T

T=14591.9 K

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