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 $\left(m\right)=2.76\times {10}^{-26}$ kg Boltzmann's constant $k_B=1.38\times {10}^{-23}J{K}^{-1})$ :

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

Answer 1

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

Given, $mass=2.7\times {10}^{-26}kg.k=1.38\times {10}^{-23}j/k$

So, $V_{es}=V_{rms}$

$11.2\times {10}^3=\sqrt{\frac{3kT}{m}}\Rightarrow T=\frac{[11.2\times {10}^3{]}^2}{3k}=\frac{[11.2\times {10}^3{]}^2}{3}\times 1.38\times {10}^{-23}=8.360\times {10}^4$