Determine the temperature at which the mean speed of the molecules of hydrogen gas becomes equal to the escape speed from the earth.

Step-by-step solution

The escape speed from the earth is v_e = 11.2 10^3 m/s . The mean speed of gas molecules is given by: v_ avg = 8RT M Equating the mean speed of hydrogen molecules to the escape speed: 8RT M = v_e Squaring both sides and solving for T : T = M v_e^2 8R For hydrogen gas, the molar mass is M = 2 10⁻³ kg/mol . Substituting the standard values ( R = 8.314 J/(mol K) ): T = 3.14 2 10⁻³ (11.2 10^3)^2 8 8.314 T = 3.14 2 125440 66.512 T 11844 K The closest value among the given options is 11800 K .