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 × 10-26 kg Boltzmann’s constant kB = 1.38 × 10-23 J K-1)

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 molecule (m) = 2.76 × 10-26 kg Boltzmann’s constant kB = 1.38 × 10-23 J K-1) (A) 1.254 × 104 K  (B) 2.508 × 104 K  (C) 5.016 × 104 K  (D) 8.360 × 104 K

Tardigrade Admin · Accepted Answer

V textescape = 11200 m/s Say at temperature T it attains V textescape So, √(3kBT/mo2 ) =11200 m/s On solving, T = 8.360 × 104 K

Q. 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 $(m) = 2.76 \times 1 0^{- 26} k g$
Boltzmann’s constant $k_{B} = 1.38 \times 1 0^{- 23} J K^{- 1}$ )

$1.254 \times 1 0^{4} K$

$2.508 \times 1 0^{4} K$

$5.016 \times 1 0^{4} K$

$8.360 \times 1 0^{4} K$

$V_{escape} = 11200 m / s$
Say at temperature T it attains $V_{escape}$
So, $\frac{3 k _{B} T}{m _{o_{2}}} = 11200 m / s$
On solving,
$T = 8.360 \times 1 0^{4} K$

Q. 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)=2.76×10−26kg Boltzmann’s constant kB​=1.38×10−23JK−1)

1.254×104K

2.508×104K

5.016×104K

8.360×104K