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# Calculate the temperature if helium atoms have an rms speed equal to the escape velocity from the surface of the Earth (11.2km/s)?

Answer : 2.01 $\times$ 10$^{4}$ K
$v_{rms} =\sqrt{ \large\frac{ 3RT}{M}}$$= 11.2 \times 10^3\; m/s \Rightarrow T = \large\frac{v_{rms}^2 \times M}{3r}$$ = \large\frac{(11.2\times 10^3)^2 \times 4 \times 10^{-3}}{3 \times 8.315}$$= 2.01 \times 10^4\;K$
edited Aug 9, 2014