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In kinetic theory of ideal gas mean speed also known as average speed is given as

Where R=gas constant=8.31Jmol^-1K^-1

T-temperature of gas

M=molar mass of gas

Molar mass of hydrogen=2amu=2g/mol=2kg/mol

Escape speed of earth is the speed given to projectile so that it escapes the gravitational field of earth. It is given by formula

Where G=universal gravitational constant

M_E=mass of earth

R=radius of earth

We also know that acceleration due to gravity g is

Multiplying and dividing equation (II) by R

Putting the value of g from equation (III) to above equation we get

According to question v_mean is equal to v_e

So, from equation (I) and (IV) we get

Radius of earth R=6400km=6400000m

g=9.8m/s

Squaring both sides

Temperature at which the mean sped of the molecules of hydrogen gas equals the escape speed from the earth is 11800K.