Question

At what temperature will the rms speed of oxygen molecules becomes just sufficient to escape from the earth's atmosphere?(Given: Mass of oxygen molecule $\left(m\right)=2.76\times {10}^{-26}kg$, Boltzmann constant i.e. $k_B=1.38\times {10}^{-23}J{K}^{-1}$)

• 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

The correct option is D $8.360\times {10}^{4}K$

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

$V_{rms}=\sqrt{\frac{3KT}{m}}$

$=11200m/s$

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

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