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) $5.016 \times 10^{4} K$

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Answer:

Correct Answer: 12. (b)

Solution:

  1. (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,

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