At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Mass of oxygen molecules (m)=2.76xx10^(-26) kg Boltzmann's constant (k_(B))=1.38xx10^(-23)JK^(-1))

At what temperature will the rms speed of oxygen molecules become just

1.	At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere? (Mass of oxygen molecules (m)=2.76xx10^(-26) kg Boltzmann's constant (k_(B))=1.38xx10^(-23)JK^(-1))
Answer» Solution :`nu_("ESCAPE")=11200ms^(-1)` Say at temperature T it attains `nu_("escape")` `nu_("escape")=sqrt((3k_(B)T)/m_(O_(2)))` `T=((nu_("escape"))^(2)xxm_(0_(2)))/(3k_(B))=((11200)^(2)xx2.76xx10^(-26))/(3xx1.38xx10^(-23))` `(3.46xx10^(8)xx10^(-26))/(4.14xx10^(-23))=0.8357xx10^(5)` `T=8.357xx10^(4)K`