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  • Find the temperature at which the mean speed of the molecules of hydrogen gas is equal to its escape speed from the earth.Option: 1 11800 K

Find the temperature at which the mean speed of the molecules of hydrogen gas is equal to its escape speed from the earth.

Option: 1

11800 K


Option: 2

 

12800 K


Option: 3

 

13800 K


Option: 4

 

11700 K


Answers (1)

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\begin{aligned} & \text { Mean speed of the molecule }=\sqrt{\frac{8 \mathrm{RT}}{\pi \mathrm{M}}} \\ & \text { Escape velocity }=\sqrt{2 \mathrm{gr}} \\ & \sqrt{\frac{8 \mathrm{RT}}{\pi \mathrm{M}}}=\sqrt{2 \mathrm{gr}} \Rightarrow \frac{8 \mathrm{RT}}{\pi \mathrm{M}}=2 \mathrm{gr} \\ & \Rightarrow \mathrm{T}=\frac{2 \mathrm{gr} \pi \mathrm{M}}{8 \mathrm{R}}=\frac{2 \times 9.8 \times 6400000 \times 3.14 \times 2 \times 10^{-3}}{8 \times 8.3}=11863.9 \approx 11800 K \end{aligned}

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