Kinetic Theory - Result Question 12
12. 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 $.k_B=1.38 \times 10^{-23} JK^{-1})$
[2018]
(a) $2.508 \times 10^{4} K$
(b) $8.360 \times 10^{4} K$
(c) $1.254 \times 10^{4} K$
(d) $5.016 \times 10^{4} K$
Show Answer
Answer:
Correct Answer: 12. (b)
Solution:
- (b) Let at temperature $T rms$ speed of oxygen molecules become just sufficient for escaping from the Earth’s atmosphere
$V _{\text{escape }}=11200 m / s$
Also, $V _{rms}=V _{\text{escape }}=\sqrt{\frac{3 k_B T}{m _{O_2}}}=11200 m / s$
Putting value of $K_B$ and $m _{O_2}$ we get,
$T=8.360 \times 10^{4} K$
