Question

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere?(Given: Mass of oxygen molecule(m)$=2.76\times {10}^{-26}$kg
Boltzmann's constant $k_B=1.38\times {10}^{-23}J{K}^{-1}$)

• A. $5.016\times {10}^4$K
• B. $2.508\times {10}^4$K
• C. $1.254\times {10}^4$K
• D. $8.360\times {10}^4$K

Answer 1

Answer: (D)

$8.360\times {10}^4$K

Since, $V_{esc}=11.2km/s$

R.M.S. = $\sqrt{\frac{3KT}{M}}$

$\sqrt{\frac{3KT}{M}}=11200$

$T=\frac{{11200}^2\times 2.76\times {10}^{-26}}{3\times 1.38\times {10}^{-23}}$

$T=8.360\times {10}^{4}K$